{"id":14374,"date":"2025-12-24T17:19:57","date_gmt":"2025-12-24T08:19:57","guid":{"rendered":"https:\/\/math-travel.com\/?p=14374"},"modified":"2026-02-11T16:41:52","modified_gmt":"2026-02-11T07:41:52","slug":"menelaus-theorem","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-a\/menelaus-theorem\/","title":{"rendered":"\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u899a\u3048\u65b9\uff01\u300c\u30ad\u30c4\u30cd\u300d\u306e\u5f62\u3067\u653b\u7565\u3059\u308b\u4f7f\u3044\u65b9\u3092\u4f8b\u984c\u3067\u89e3\u8aac"},"content":{"rendered":"\n
\u300c\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3063\u3066\u3069\u3093\u306a\u516c\u5f0f\uff1f\u300d
\u300c\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u4f7f\u3044\u65b9\u304c\u77e5\u308a\u305f\u3044\u300d<\/p>\n<\/div><\/div>\n\n\n\n
\u4eca\u56de\u306f\u6570\u5b661A\u306e\u56f3\u5f62\u306e\u6027\u8cea\u304b\u3089\u300c\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u300d<\/span>\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n \u56f3\u5f62\u306e\u554f\u984c\u306f\u3069\u3046\u3057\u3066\u3082\u82e6\u624b\u3067\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u3001\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u306e\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n \u25b3ABC\u3068\u76f4\u7ddaDE\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n \u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u306e\u4ea4\u70b9\u3092\u305d\u308c\u305e\u308c\u70b9D,E,F\u3067\u4ea4\u308f\u308b\u3068\u304d<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=1\\]<\/p>\n<\/div><\/div>\n\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u516c\u5f0f\u3092\u77e5\u3063\u3066\u3044\u308b\u3060\u3051\u3067\u30d1\u30c3\u3068\u7b54\u3048\u3092\u51fa\u305b\u308b\u4fbf\u5229\u306a\u516c\u5f0f\u306e1\u3064<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n \u672c\u8a18\u4e8b\u3067\u306f\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u4f7f\u3044\u65b9\u3084\u8a3c\u660e\u65b9\u6cd5\u3001\u899a\u3048\u65b9\u306a\u3069\u306b\u3064\u3044\u3066\u89e3\u8aac<\/span>\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305f\u3001\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3068\u30bb\u30c3\u30c8\u3067\u7fd2\u3046\u300c\u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u300d<\/span>\u306b\u3064\u3044\u3066\u3082\u8aac\u660e\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u5408\u308f\u305b\u3066\u53c2\u8003\u306b\u3057\u3066\u3044\u305f\u3060\u3051\u308c\u3070\u3068\u601d\u3044\u307e\u3059\uff01<\/p>\n\n\n \u5165\u587e\u3092\u691c\u8a0e\u3057\u3066\u3044\u308b\u65b9\u306f \u305d\u308c\u3067\u306f\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3068\u306f\u300c\u4e09\u89d2\u5f62\u300d\u3068\u300c\u76f4\u7dda\u300d\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u306e\u516c\u5f0f\u3067\u3059\u3002<\/span><\/span><\/p>\n\n\n \u4e0a\u753b\u50cf\u306e\u3088\u3046\u306b\u300c\u76f4\u7dda\u300d\u304c\u300c\u4e09\u89d2\u5f62\u300d\u306e\u9802\u70b9\u3092\u201c\u901a\u3089\u305a\u201d\u306b2\u70b9\u3067\u4ea4\u308f\u308b<\/span>\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n \u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u306e\u4ea4\u70b9\u3092\u305d\u308c\u305e\u308c\u70b9D,E,F\u3067\u4ea4\u308f\u308b\u3068\u304d<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=1\\]<\/p>\n\n\n\n \u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n<\/div><\/div>\n\n\n\n \u307e\u305f\u3001\u4e0a\u306e\u56f3\u3067\u306f\u3001\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u304c\u4ea4\u308f\u308b\u5834\u5408\u3067\u3059\u304c\u3001\u4ea4\u308f\u3089\u306a\u3044\u5834\u5408\u3067\u3082\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=1\\]<\/p>\n\n\n\n \u3053\u306e\u5185\u90e8\u3067\u4ea4\u308f\u3089\u306a\u3044\u30d1\u30bf\u30fc\u30f3\u306f\u3001\u306a\u304b\u306a\u304b\u7406\u89e3\u3059\u308b\u306e\u304c\u96e3\u3057\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u6163\u308c\u308b\u307e\u3067\u306f\u3001\u6700\u521d\u306b\u7d39\u4ecb\u3057\u305f\u300c\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u304c\u4ea4\u308f\u308b\u30d1\u30bf\u30fc\u30f3\u300d\u3067\u7406\u89e3\u3092\u9032\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u300c\u4e09\u89d2\u5f62\u300d\u3068\u300c\u76f4\u7dda\u300d\u306e\u554f\u984c\u304c\u51fa\u3066\u304d\u305f\u6642\u306b\u4f7f\u3048\u308b\u516c\u5f0f\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u4f55\u3068\u306a\u304f\u5206\u304b\u308a\u307e\u3059\u304c\u3001\u3061\u3087\u3063\u3068\u899a\u3048\u3065\u3089\u3044\u304b\u3082\u2026\u3068\u4e0d\u5b89\u306b\u306a\u308a\u307e\u3059\u3088\u306d\uff01<\/p>\n\n\n\n \u3053\u3053\u3067\u306f\u3001\u5b9a\u7406\u306e\u899a\u3048\u65b9\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u30ad\u30c4\u30cd\u306e\u9854\u3067\u899a\u3048\u308b\u65b9\u6cd5\u3067\u3059\u3002\u4e0b\u306e\u3088\u3046\u306b\u8d64\u3044\u90e8\u5206\u3092\u30ad\u30c4\u30cd\u306e\u8f2a\u90ed\u3068\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n \u52d5\u304d\u65b9\u3092\u78ba\u8a8d\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n 1.\u30ad\u30c4\u30cd\u306e\u982d\u2192\u8033\uff08\u4e0b\u5074\uff09\uff08\u2460\uff09\u304b\u3089\u59cb\u307e\u3063\u3066\u3001\u8033\u2192\u9014\u4e2d\uff08\u2781\uff09\u307e\u3067\u623b\u308a\u307e\u3059\u3002<\/p>\n\n\n 2.\u305d\u3053\u304b\u3089\u306f\u9806\u756a\u306b\u300c\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u306e\u4ea4\u70b9\u300d\u2192\u300c\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u300d\uff08\u2462\u2192\u2463\u2192\u2464\u2192\u2465\uff09\u3068\u3044\u3063\u305f\u9806\u756a\u3067\u3059\u3002<\/p>\n\n\n \u2460\uff5e\u2465\u3092\u5206\u5b50\u5206\u6bcd\u306b\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f53\u3066\u306f\u3081\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\displaystyle \\frac{\u2460}{\u2461} \\times \\frac{\u2462}{\u2463} \\times \\frac{\u2464}{\u2465}=1\\]<\/p>\n\n\n\n \u2460\uff5e\u2465\u306b\u7dda\u5206\u3092\u5f53\u3066\u306f\u3081\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC} \\times \\frac{CF}{FA} \\times \\frac{AD}{DB}=1\\]<\/p>\n\n\n\n \u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u306e\u9806\u756a\u3092\u8ffd\u3046\u3088\u3046\u306b\u3059\u308b\u3068\u3001\u3055\u3089\u306b\u5206\u304b\u308a\u3084\u3059\u304f\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u306e\u3067\u3001\u304a\u3059\u3059\u3081\u3067\u3059\u3002<\/p>\n\n\n B\u2192E\u2192C\u2192F\u2192A\u2192D\u2192B\u3068\u3044\u3063\u305f\u98a8\u306b\u3001\u6700\u521d\u306b\u59cb\u307e\u3063\u305f\u70b9\u306b\u623b\u3063\u3066\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u9806\u756a\u304c\u5206\u304b\u3089\u306a\u304f\u306a\u3063\u305f\u5834\u5408\u306e\u53c2\u8003\u306b\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n \u30ad\u30c4\u30cd\u304c\u5206\u304b\u308a\u3065\u3089\u3044\u4eba\u305f\u3081\u306b\u5225\u306e\u899a\u3048\u65b9\u3082\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305a\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u3068\u3001\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u70b9\u3092\u5206\u3051\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u3053\u3067\u306f\u3001\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u3092 \u3007\u3001\u76f4\u7dda\u4e0a\u306e\u70b9\u3092 \u2606 \u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n \u305d\u3057\u305f\u3089\u3001\u70b9B\u304b\u3089\u59cb\u3081\u3066\u3001\u300c\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u306e\u4ea4\u70b9\u300d\u3068\u300c\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u300d\u3068\u3092\u4ea4\u4e92\u306b\u7d50\u3073\u307e\u3059\u3002<\/p>\n\n\n\n \u3007\u2192\u2606\u2192\u3007\u2192\u2606\u2192\u3007\u2192\u2606\u2192\u3007\u3068\u3044\u3046\u30a4\u30e1\u30fc\u30b8\u3067\u3059\u3002<\/p>\n\n\n\n \u3059\u308b\u3068\u3001\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u5f0f\u304c\u51fa\u6765\u4e0a\u304c\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC} \\times \\frac{CF}{FA} \\times \\frac{AD}{DB}=1\\]<\/p>\n\n\n\n \u3053\u306e\u899a\u3048\u65b9\u3092\u7406\u89e3\u3057\u3066\u304a\u304f\u3068\u3001\u300c\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u304c\u4ea4\u308f\u3089\u306a\u3044\u5834\u5408\u3067\u3082\u300d\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3092\u7406\u89e3\u3057\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u3053\u3067\u3001\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u3092 \u3007\u3001\u76f4\u7dda\u4e0a\u306e\u70b9\u3092 \u2606 \u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n \u305d\u3057\u305f\u3089\u3001\u70b9B\u304b\u3089\u59cb\u3081\u3066\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u3068\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u70b9\u3092\u4ea4\u4e92\u306b\u7d50\u3073\u307e\u3059\u3002<\/p>\n\n\n\n \u5148\u307b\u3069\u3068\u540c\u3058\u3088\u3046\u306b\u3007\u2192\u2606\u2192\u3007\u2192\u2606\u2192\u3007\u2192\u2606\u2192\u3007\u3068\u3044\u3046\u30a4\u30e1\u30fc\u30b8\u3067\u3059\u3002<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC} \\times \\frac{CF}{FA} \\times \\frac{AD}{DB}=1\\]<\/p>\n\n\n \u50d5\u306f\u899a\u3048\u65b9\u2461\u306e\u307b\u3046\u304c\u5206\u304b\u308a\u3084\u3059\u304b\u3063\u305f\u3067\u3059\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u3001\u56f3\u5f62\u304c\u7d61\u3093\u3067\u3044\u308b\u554f\u984c\u3067\u300c\u7dda\u5206\u306e\u6bd4\u30fb\u9577\u3055\u300d\u3092\u6c42\u3081\u308b\u5834\u5408\u306b\u4f7f\u3046<\/span>\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002<\/p>\n\n\n\n \u4ee5\u4e0b\u306e\u4f8b\u984c\u3067\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u4f7f\u3044\u65b9\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u8fbaAB\u30923:2\u306b\u5185\u5206\u3059\u308b\u70b9\u3092D\u3001\u8fbaAC\u30924:1\u306b\u5185\u5206\u3059\u308b\u70b9\u3092F\u3068\u3059\u308b\u3002 \u3053\u308c\u3092\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\uff01<\/p>\n\n\n\n \u307e\u305a\u3001\u7dda\u5206\u306b\u95a2\u3059\u308b\u60c5\u5831\u3092\u6574\u7406\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u8fbaAB\u30923:2\u306b\u5185\u5206\u3059\u308b\u70b9\u3092D\u3000\u2192\u3000AD:DB=3:2<\/p>\n\n\n\n \u8fbaAC\u30924:1\u306b\u5185\u5206\u3059\u308b\u70b9\u3092F\u3000\u2192\u3000AF:FC=4:1<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u3053\u3067ABC\u306b\u6ce8\u76ee\u3057\u3066\u307f\u308b\u3068\u3001\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u304c\u4f7f\u3048\u307e\u3059\u3002<\/p>\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3088\u308a\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC} \\times \\frac{CF}{FA} \\times \\frac{AD}{DB}=1\\]<\/p>\n\n\n\n \u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u3053\u306b\u5206\u304b\u3063\u3066\u3044\u308b\u60c5\u5831\u3092\u4ee3\u5165\u3057\u3066\u307f\u308b\u3068<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC} \\times \\frac{1}{4} \\times \\frac{3}{2}=1\\]<\/p>\n\n\n\n \u3053\u306e\u5f0f\u3092\u89e3\u304f\u3068\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC}=\\frac{8}{3}\\]<\/p>\n\n\n\n \u3088\u3063\u3066\u3001BE:EC=8:3\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n \u56f3\u5f62\u304b\u3089\u5206\u304b\u308b\u60c5\u5831\u3092\u4ee3\u5165\u3057\u305f\u3089\u89e3\u3051\u307e\u3057\u305f\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u3053\u3053\u3067\u306f2\u3064\u306e\u65b9\u6cd5\u3067\u3001\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3092\u8a3c\u660e\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u3042\u308b\u300c\u76f4\u7dda\u300d\u304c\u300c\u4e09\u89d2\u5f62\u300d\u306e\u9802\u70b9\u3092\u201c\u901a\u3089\u305a\u201d\u306b 2\u70b9\u3067\u4ea4\u308f\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n \u56f3\u306b\u304a\u3044\u3066\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=1\\]<\/p>\n\n\n\n \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n \u3010\u8a3c\u660e\u3011<\/p>\n\n\n\n \u76f4\u7dda\u306b\u5e73\u884c\u306a\u7dda\u304b\u3064\u3001\u70b9C\u3092\u901a\u308b\u76f4\u7dda\u3092\u5f15\u304d\u3001\u3053\u306e\u76f4\u7dda\u3068\u8fbaAB\u3068\u306e\u4ea4\u70b9\u3092P\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n DE\/\/PC\u3001DF\/\/PC\u3088\u308a\u3001<\/p>\n\n\n\n \\[BE:EC=BD:DP\\]<\/p>\n\n\n\n \u3088\u3063\u3066\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC} = \\frac{BD}{DP} \\cdots \u2460\\]<\/p>\n\n\n\n \u307e\u305f\u3001\u540c\u69d8\u306b\u3001PD:DA=CF:FA<\/p>\n\n\n\n \u3088\u3063\u3066\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{PD}{DA} = \\frac{CF}{FA} \\cdots \u2461\\]<\/p>\n\n\n\n \u2460\u2781\u3088\u308a<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC} \\times \\frac{CF}{FA} =\\frac{BD}{DP} \\times \\frac{PD}{DA}\\]<\/p>\n\n\n\n \u4e21\u8fba\u306b\\(\\displaystyle \\frac{AD}{DB}\\)\u3092\u639b\u3051\u3066<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=\\frac{AD}{DB} \\times \\frac{BD}{DP} \\times \\frac{PD}{DA}\\]<\/p>\n\n\n\n \u3053\u3053\u3067<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BD}{DP} \\times \\frac{PD}{DA}=1\\]<\/p>\n\n\n\n \u306a\u306e\u3067\u3001\u5de6\u8fba\u3082\u540c\u69d8\u306b<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=1\\]<\/p>\n\n\n\n \u3068\u306a\u308a\u3001\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n \u5e73\u884c\u7dda\u3092\u5f15\u3044\u3066\u3001\u8fba\u306e\u6bd4\u3067\u8a3c\u660e\u3059\u308b\u3093\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u4e0a\u8a18\u753b\u50cf\u306b\u304a\u3044\u3066\u3001<\/p>\n\n\n\n \\[\\triangle{BFE}=p\\]<\/p>\n\n\n\n \\[\\triangle{CFE}=q\\]<\/p>\n\n\n\n \\[\\triangle{AFE}=r\\]<\/p>\n\n\n\n \u3068\u3059\u308b\u3002<\/p>\n\n\n\n \\(\\triangle{BFE}\\)\u3068\\(\\triangle{CFE}\\)\u306f\u9ad8\u3055\u304c\u540c\u3058\u4e09\u89d2\u5f62\u3067\u3042\u308a\u3001\u3053\u306e\u5834\u5408\u3001\u5e95\u8fba\u306e\u9577\u3055\u306e\u6bd4=\u9762\u7a4d\u6bd4\u3068\u6210\u308a\u7acb\u3064\u306e\u3067\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{CE}=\\frac{p}{q} \\cdots \u2460\\]<\/p>\n\n\n\n \u540c\u69d8\u306b\u3001\\(\\triangle{CFE}\\)\u3068\\(\\triangle{AFE}\\)\u3082\u9ad8\u3055\u304c\u540c\u3058\u4e09\u89d2\u5f62\u3067\u3042\u308b\u305f\u3081\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{CF}{AF}=\\frac{q}{r} \\cdots \u2781\\]<\/p>\n\n\n\n \u307e\u305f\u3001\\(\\triangle{AFE}\\)\u3068\\(\\triangle{BFE}\\)\u306f\u3001\u8fbaFE\uff08\u5e95\u8fba\uff09\u304c\u5171\u901a\u306e\u4e09\u89d2\u5f62\u3067\u3042\u308b\u3002<\/p>\n\n\n\n \u5e95\u8fba\u304c\u5171\u901a\u306e\u4e09\u89d2\u5f62\u306e\u5834\u5408\u3001\u9ad8\u3055\u306e\u6bd4=\u9762\u7a4d\u6bd4\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3088\u306d\u3002<\/p>\n\n\n \u3053\u306e\u9ad8\u3055\u306e\u6bd4\u306f\u7dda\u5206AD\u3001DB\u306e\u6bd4\u3068\u7b49\u3057\u3044\u306e\u3067\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB}=\\frac{r}{p} \\cdots \u2782\\]<\/p>\n\n\n\n \u2460\u2781\u2782\u3088\u308a\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{BE}{EC} \\times \\frac{CF}{FA} \\times \\frac{AD}{DB}=\\frac{p}{q} \\times \\frac{q}{r} \\times \\frac{r}{p}=1\\]<\/p>\n\n\n\n \u3068\u306a\u308a\u3001\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n \u9762\u7a4d\u6bd4\u3068\u8fba\u306e\u6bd4\u3092\u7528\u3044\u3066\u8a3c\u660e\u3057\u3066\u3044\u307e\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u305f\u7df4\u7fd2\u554f\u984c\u306b\u6311\u6226\u3057\u3001\u516c\u5f0f\u306e\u4f7f\u3044\u65b9\u3092\u5b9a\u7740\u3055\u305b\u307e\u3057\u3087\u3046\uff01<\/p>\n\n\n\n \u4e0b\u306e\u56f3\u306b\u304a\u3044\u3066\u3001\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n (BC:CE=3:2)<\/p>\n\n\n\n (AD:DB=1:5)<\/p>\n\n\n\n \u3053\u306e\u3068\u304d\u3001\u7dda\u5206CF\u3068FA\u306e\u6bd4\u3092\u6c42\u3081\u3088\u3002<\/p>\n<\/div><\/div>\n\n\n\n \u89e3\u7b54<\/p>\n\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3088\u308a\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=1\\]<\/p>\n\n\n\n \u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n\n \u3088\u3063\u3066\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{1}{5} \\times \\frac{5}{2} \\times \\frac{CF}{FA}=1\\]<\/p>\n\n\n\n \u3053\u308c\u3092\u89e3\u304f\u3068\u3001CF:FA=2:1<\/p>\n\n\n\n \u89e3\u3051\u307e\u3057\u305f\u3067\u3057\u3087\u3046\u304b\uff1f \u4e0b\u306e\u56f3\u306b\u304a\u3044\u3066\u3001\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n (DF:FE=1:1)<\/p>\n\n\n\n (AD:DB=3:2)<\/p>\n\n\n\n \u7dda\u5206BC\u3068CE\u306e\u6bd4\u3092\u6c42\u3081\u3088\u3002<\/p>\n<\/div><\/div>\n\n\n\n \u3053\u306e\u5834\u5408\u306f\\(\\triangle{EDB}\\)\u306b\u76f4\u7ddaCA\u304c\u523a\u3055\u3063\u3066\u3044\u308b\u3068\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n \u306a\u306e\u3067\u3001\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\displaystyle \\frac{EC}{CB} \\times \\frac{BA}{AD} \\times \\frac{DF}{FE}=1\\]<\/p>\n\n\n\n \u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n\n\n\n \u3088\u3063\u3066\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{EC}{CB} \\times \\frac{5}{3} \\times \\frac{1}{1}=1\\]<\/p>\n\n\n\n \u3053\u308c\u3092\u89e3\u304f\u3068\u3001BC:CE=5:3<\/p>\n\n\n \u5411\u304d\u304c\u5909\u308f\u308b\u3068\u307e\u3060\u6df7\u4e71\u3057\u307e\u3059<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n \u554f\u984c\u7528\u7d19\u306e\u5411\u304d\u3092\u5909\u3048\u3066\u898b\u3084\u3059\u3044\u5411\u304d\u306b\u3059\u308b\u3068\u826f\u3044\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3068\u540c\u30bf\u30a4\u30df\u30f3\u30b0\u3067\u7fd2\u3046\u306e\u304c\u300c\u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u300d<\/span>\u3067\u3059\u3088\u306d\uff01<\/p>\n\n\n\n \u3068\u3044\u3046\u3053\u3068\u3067\u3001\u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u306b\u3064\u3044\u3066\u3082\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u306f\u3001\u4e09\u89d2\u5f62\u306e\u5404\u9802\u70b9\u304b\u3089\u5bfe\u8fba\u306b\u5f15\u3044\u305f\u7dda\u5206\u304c1\u70b9\u3067\u4ea4\u308f\u308b\u3068\u304d<\/span>\u306b\u3001\u8fba\u306e\u7dda\u5206\u306e\u6bd4\u306b\u5bfe\u3057\u3066\u6210\u308a\u7acb\u3064\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u3068\u304d\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=1\\]<\/p>\n\n\n\n \u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n<\/div><\/div>\n\n\n \u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u306f\u5468\u56f2\u3092\u30b0\u30eb\u3063\u3068\u56de\u308b\u3060\u3051\u3060\u304b\u3089\u899a\u3048\u3084\u3059\u3044\u3067\u3059\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u3068\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u4f3c\u3066\u3044\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u306e\u4f7f\u3044\u5206\u3051\u306f\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u306e\u95a2\u4fc2\u304c\u30dd\u30a4\u30f3\u30c8<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u3001\u300c\u4e09\u89d2\u5f62\u300d\u3068\u300c\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u3092\u901a\u3089\u306a\u3044\u76f4\u7dda\u300d\u304c\u3042\u308b\u56f3\u5f62\u306e\u554f\u984c\u306b\u5bfe\u3057\u3066\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u3092\u901a\u3089\u306a\u3044\u76f4\u7dda\u306b\u3064\u3044\u3066\u306f\u3001\u4e09\u89d2\u5f62\u306e\u5916\u90e8\u3092\u901a\u308b\u5834\u5408\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305f\u3001\u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u306f\u300c\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u304b\u3089\u5bfe\u8fba\u3078\u4e0b\u308d\u3057\u305f3\u7dda\u304c\u4ea4\u5dee\u3059\u308b\u56f3\u5f62\u300d\u306e\u554f\u984c\u306b\u5bfe\u3057\u3066\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n \u4eca\u56de\u306f\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n \u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u306e\u4ea4\u70b9\u3092\u305d\u308c\u305e\u308c\u70b9D,E,F\u3067\u4ea4\u308f\u308b\u3068\u304d<\/p>\n\n\n\n \\[\\displaystyle \\frac{AD}{DB} \\times \\frac{BE}{EC} \\times \\frac{CF}{FA}=1\\]<\/p>\n<\/div><\/div>\n\n\n\n \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u899a\u3048\u65b9\u306f2\u3064\u3042\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n 2\u3064\u306e\u5b9a\u7406\u306e\u4f7f\u3044\u5206\u3051\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n \u30fb\u30c1\u30a7\u30d0\u306e\u5b9a\u7406 \u30fb\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406 \u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u3068\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u3069\u3061\u3089\u3082\u8fba\u306e\u6bd4\u3084\u9577\u3055\u3092\u6c42\u3081\u308b\u6642\u306b\u4f7f\u3046\u306e\u3067\u3001\u4e09\u89d2\u5f62\u306e\u8fba\u306e\u6bd4\u3084\u9577\u3055\u3092\u805e\u304b\u308c\u305f\u3089\u3001\u3053\u306e2\u3064\u306e\u5b9a\u7406\u3092\u601d\u3044\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\uff01<\/p>\n\n\n\n \u53cd\u5fa9\u7df4\u7fd2\u3057\u3066\u3044\u3051\u3070\u5fc5\u305a\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308b\u306e\u3067\u5b66\u6821\u306e\u554f\u984c\u96c6\u3067\u305f\u304f\u3055\u3093\u7df4\u7fd2\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u4eca\u56de\u306f\u6570\u5b661A\u306e\u56f3\u5f62\u306e\u6027\u8cea\u304b\u3089\u300c\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u300d\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u3001\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u306e\u516c\u5f0f\u3067\u3059\u3002 \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306f\u516c\u5f0f\u3092\u77e5\u3063\u3066\u3044\u308b\u3060\u3051\u3067\u30d1\u30c3\u3068\u7b54\u3048\u3092\u51fa\u305b\u308b\u4fbf\u5229\u306a\u516c\u5f0f\u306e1\u3064\u3067 […]<\/p>\n","protected":false},"author":1,"featured_media":14404,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[29,223],"tags":[28,10,11],"class_list":["post-14374","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-zukei","category-math-a","tag-28","tag-a","tag-11"],"yoast_head":"\n
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>
\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3068\u306f<\/h2>\n\n\n\n

\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\uff08\u4e09\u89d2\u5f62\u3068\u76f4\u7dda\u304c\u4ea4\u308f\u3089\u306a\u3044\u5834\u5408\uff09<\/h3>\n\n\n

\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u899a\u3048\u65b9<\/h2>\n\n\n\n
\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u899a\u3048\u65b9\u2460<\/h3>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u899a\u3048\u65b9\u2461<\/h3>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u4f7f\u3044\u65b9<\/h2>\n\n\n\n
\u3053\u306e\u3068\u304d\u3001BE:EC\u3092\u6c42\u3081\u3088\u3002<\/p>\n\n\n\n
<\/p>\n<\/div><\/div>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u306e\u8a3c\u660e\u65b9\u6cd5<\/h2>\n\n\n\n
\u8a3c\u660e\u2460\u5e73\u884c\u7dda\u3068\u6bd4\u306e\u5b9a\u7406\u3067\u8003\u3048\u308b<\/h3>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\u8a3c\u660e\u2461\u9762\u7a4d\u306e\u6bd4\u3067\u8003\u3048\u308b<\/h3>\n\n\n
<\/figure>\n<\/div>\n\n\n
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\u9ad8\u6821\u751f<\/span><\/div>\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\uff1c\u7df4\u7fd2\u554f\u984c\uff1e<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
\u3082\u30461\u554f\u3084\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>\u30c1\u30a7\u30d0\u306e\u5b9a\u7406<\/h2>\n\n\n\n
\u30c1\u30a7\u30d0\u306e\u5b9a\u7406<\/h3>\n\n\n\n
<\/p>\n\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3068\u306e\u4f7f\u3044\u5206\u3051<\/h3>\n\n\n\n
<\/figure>\n<\/div>\n
<\/figure>\n<\/div>\n<\/div>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n

\n
\u21d2\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u304b\u3089\u5bfe\u8fba\u3078\u4e0b\u308d\u3057\u305f3\u7dda\u304c\u4ea4\u5dee\u3059\u308b\u56f3\u5f62<\/p>\n\n\n\n
\u21d2\u300c\u4e09\u89d2\u5f62\u300d\u3068\u300c\u4e09\u89d2\u5f62\u306e\u9802\u70b9\u3092\u901a\u3089\u306a\u3044\u76f4\u7dda\u300d\u304c\u3042\u308b\u56f3\u5f62\u306e\u554f\u984c<\/p>\n<\/div><\/div>\n\n\n\n