{"id":1714,"date":"2025-12-24T17:19:57","date_gmt":"2025-12-24T08:19:57","guid":{"rendered":"https:\/\/math-travel.com\/?p=1714"},"modified":"2026-02-11T16:54:51","modified_gmt":"2026-02-11T07:54:51","slug":"orthocenter","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-a\/orthocenter\/","title":{"rendered":"\u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u3068\u306f\uff1f\u6027\u8cea\u3068\u8a3c\u660e\uff1a3\u3064\u306e\u5782\u7dda\u304c1\u70b9\u3067\u4ea4\u308f\u308b\u7406\u7531\u3092\u308f\u304b\u308a\u3084\u3059\u304f"},"content":{"rendered":"\n
\u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u304c\u3044\u307e\u3044\u3061\u306a\u65b9\u306f\u5fc5\u898b\u3067\u3059\uff01<\/span><\/p>\n\n\n\n \u4eca\u56de\u306f\u5782\u5fc3\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u500b\u5225\u6307\u5c0e\u6b7410\u5e74\u306e\u6570\u5b66\u8b1b\u5e2b\u304c\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u304c\u3088\u304f\u5206\u304b\u3089\u306a\u304f\u3066\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n \u4e09\u89d2\u5f62\u306b\u306f\u4e94\u5fc3\u3068\u547c\u3070\u308c\u308b5\u3064\u306e\u70b9<\/span>\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u3068\u306f\u3001\u5404\u9802\u70b9\u304b\u3089\u5bfe\u8fba\u306b\u5411\u304b\u3063\u3066\u5782\u7dda\u3092\u5f15\u3044\u305f\u4ea4\u70b9<\/span>\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n \u672c\u8a18\u4e8b\u3067\u306f\u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u306e\u5b9a\u7fa9\u3084\u6027\u8cea\u306b\u3064\u3044\u3066\u89e3\u8aac<\/span>\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u3059\u3079\u3066\u89e3\u6c7a\u3067\u304d\u308b\u3088\u3046\u306b\u89e3\u8aac\u3057\u305f\u306e\u3067\u3001\u305c\u3072\u6700\u5f8c\u307e\u3067\u898b\u3066\u3044\u3063\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u3068\u306f\u3001\u4e09\u89d2\u5f62\u306e\u5404\u9802\u70b9\u304b\u3089\u5bfe\u8fba\u306b\u5411\u304b\u3063\u3066\u3072\u3044\u305f\u5782\u7dda\u306e\u4ea4\u70b9<\/span>\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n \u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e09\u89d2\u5f62\\(ABC\\)\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n \u4e09\u89d2\u5f62\u306e\u5404\u9802\u70b9\u304b\u3089\u5bfe\u8fba\u306b\u5411\u304b\u3063\u3066\u5782\u7dda\u3092\u5f15\u304d\u307e\u3059\u3002<\/p>\n\n\n \u3059\u308b\u30683\u672c\u306e\u5782\u7dda\u304c\uff11\u70b9\u3067\u4ea4\u308f\u308a\u3001\u305d\u306e\u70b9\u3092\u4e09\u89d2\u5f62\u306e\u5782\u5fc3<\/span>\u3068\u3088\u3073\u307e\u3059\u3002<\/p>\n\n\n \u5782\u7dda\u306e\u4ea4\u70b9\u3060\u304b\u3089\u5782\u5fc3\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n \u5782\u5fc3\u306e\u5b9a\u7fa9\u306f\u5206\u304b\u308a\u3084\u3059\u304f\u3066\u3044\u3044\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u5782\u7dda\u304c1\u70b9\u3067\u4ea4\u308f\u308b\u3053\u3068\u306e\u8a3c\u660e\u306f\u3001\u300c2\u672c\u306e\u5782\u7dda\u306e\u4ea4\u70b9\u3092\uff13\u672c\u76ee\u306e\u5782\u7dda\u3082\u901a\u904e\u3059\u308b\u300d<\/span>\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305a\u306f\uff12\u672c\u306e\u5782\u7dda\u304c\u3042\u308a\u3001\u305d\u306e\u4ea4\u70b9\u3092\u4ea4\u70b9H\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u305d\u306e\u3042\u3068\u4ea4\u70b9H\u3092\u901a\u904e\u3059\u308b\u3088\u3046\u306b\u7dda\u5206CD\u3092\u5f15\u3044\u305f\u3082\u306e\u304c\u4e0b\u56f3\u3067\u3059\u3002<\/p>\n\n\n \u3053\u306e\u6bb5\u968e\u3067\u306f\u307e\u3060\\(\\angle CDA\\)\u304c\u5782\u76f4\u3068\u306f\u5206\u304b\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n \u305d\u3053\u3067\u3001\u7dda\u5206CD\u304c\u5782\u76f4\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3067\u304d\u308c\u3070\u30013\u672c\u306e\u5782\u7dda\u304c\uff11\u70b9\u3067\u4ea4\u308f\u308b\u3053\u3068\u3092\u793a\u305b\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \\(\\angle CFH,\\angle CEH\\)\u306f\u3068\u3082\u306b\u76f4\u89d2\u306a\u306e\u3067\u3001 C, F, H, E \u306e4\u70b9\u306f\u3001CH\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u5468\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u3053\u3068\u304b\u3089\u3001\u5186\u5468\u89d2\u306e\u5b9a\u7406\u3088\u308a<\/p>\n\n\n\n \\(\\angle HCF=\\angle HEF\\)\u304c\u8a00\u3048\u307e\u3059\u3002(\u4e0b\u56f3\u3092\u53c2\u8003\u306b\u3057\u3066\u304f\u3060\u3055\u3044)<\/p>\n\n\n \u307e\u305f\u3001\\(\\angle AEB,\\angle AFB\\)\u3082\u3068\u3082\u306b\u76f4\u89d2\u306a\u306e\u3067\u3001 A, B, E, F \u306e4\u70b9\u306f\u3001AB\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u5468\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u3053\u3068\u304b\u3089\u3001\\(\\angle AEF=\\angle ABF\\)\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n \u3088\u3063\u3066\u3001<\/p>\n\n\n\n 2\u3064\u3092\u5408\u308f\u305b\u308b\u3068\u3001\\(\\angle ACD=\u2220ABF\\)\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001\uff13\u672c\u306e\u5782\u7dda\u304c\uff11\u70b9\u3067\u4ea4\u308f\u308b\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u306b\u306f\uff12\u3064\u306e\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305a\u6027\u8cea\u3092\u7d39\u4ecb\u3057\u3066\u304b\u3089\u8a3c\u660e\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \uff11\uff1a\u56db\u89d2\u5f62ADHF,BEHD,CFHE\u306f\u5186\u306b\u5185\u63a5\u3059\u308b\u56db\u89d2\u5f62\u3067\u3042\u308b<\/span><\/p>\n\n\n \uff12\uff1a\\(AH=2R\\cos A\\)<\/span> \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u304c\u3082\u3064\u6027\u8cea\u306e\u8a3c\u660e\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u307e\u305a\u306f\u300c\u56db\u89d2\u5f62ADHF,BEHD,CFHE\u306f\u5186\u306b\u5185\u63a5\u3059\u308b\u56db\u89d2\u5f62\u3067\u3042\u308b<\/span>\u300d\u3092\u8a3c\u660e\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u308c\u306b\u306f\u3001\u4e2d\u5b663\u5e74\u751f\u3067\u7fd2\u3063\u305f\u5186\u5468\u89d2\u306e\u5b9a\u7406<\/span>\u3092\u4f7f\u3046\u3068\u7406\u89e3\u304c\u65e9\u3044\u3067\u3059\u3002<\/p>\n\n\n\n \u56db\u89d2\u5f62CFHE\u306b\u6ce8\u76ee\u3059\u308b\u3068\u3001\\(\\angle CFH=90^\\circ\\),\\(\\angle CEH=90^\\circ\\)<\/p>\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001\u5186\u5468\u89d2\u306e\u5b9a\u7406\u306e\u9006\u3092\u7528\u3044\u3066\u3001CH\u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u304c\u898b\u3048\u3066\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u4ed6\u306e\u56db\u89d2\u5f62\u3067\u3082\u540c\u69d8\u306e\u8a3c\u660e\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u3064\u304e\u306b\u5782\u5fc3\u306e\u6027\u8cea\uff12\u300c\\(AH=2R\\cos A\\)<\/span>\u300d\u306e\u8a3c\u660e\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u308c\u306f\u4e09\u89d2\u95a2\u6570\u306e\u6b63\u5f26\u5b9a\u7406\u3092\u7528\u3044\u3066\u8a3c\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u4e09\u89d2\u5f62ABC\u306e\u5916\u63a5\u5186\u306e\u534a\u5f84\u3092\\(R\\)\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n \\(AH=\\displaystyle \\frac{AF}{\\cos \\angle CAE}\\)<\/p>\n\n\n\n \\(AF=AB\\cos A\\)<\/p>\n\n\n\n \\(\\cos \\angle CAE=\\sin(90^\\circ-\\angle CAE)=\\sin \\angle ACE\\)<\/p>\n\n\n\n \u306a\u306e\u3067\u3001<\/p>\n\n\n\n \\[\\displaystyle \\frac{AF}{\\cos \\angle CAE}=\\displaystyle \\frac{AB\\cos A}{\\sin \\angle ACE}\\]<\/p>\n\n\n \u4e09\u89d2\u5f62ABC\u306e\u5916\u63a5\u5186\u306e\u534a\u5f84\u3092R\u3068\u3057\u305f\u3068\u304d\u3001<\/p>\n \\[\\displaystyle \\frac{a}{\\sin A}=\\frac{b}{\\sin B}=\\frac{c}{\\sin C}=2R\\]<\/p>\n<\/div>\n\n\n\n \u6b63\u5f26\u5b9a\u7406\u306b\u3064\u3044\u3066\u77e5\u308a\u305f\u3044\u65b9\u306f\u300c\u6b63\u5f26\u5b9a\u7406\u306e\u516c\u5f0f\u3068\u8a3c\u660e\u300d\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n \u6b63\u5f26\u5b9a\u7406\u3088\u308a<\/p>\n\n\n\n \\[\\displaystyle \\frac{AB\\cos A}{\\sin \\angle ACE}=2R\\cos A\\]<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n \\[AH=2R\\cos A\\]<\/p>\n\n\n\n \u8a3c\u660e\u7d42\u4e86\u3002<\/p>\n\n\n\n \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u306f\u4f5c\u56f3\u3060\u3051\u3067\u306a\u304f\u3001\u5ea7\u6a19\u3084\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u8d85\u57fa\u672c\u3067\u3059\u304c\u5b9f\u969b\u306b\u5782\u7dda\u3092\u5f15\u3044\u3066\u5782\u7dda\u3092\u898b\u3064\u3051\u307e\u3059\u3002<\/p>\n\n\n\n \u5fc5\u8981\u306a\u306e\u306f\u3001\u4e09\u89d2\u5f62\u3001\u7b46\u8a18\u7528\u5177\u3001\u30b3\u30f3\u30d1\u30b9<\/span>\u3067\u3059\u3002<\/p>\n\n\n \u3069\u3053\u304b\u306e\u9802\u70b9\u306b\u30b3\u30f3\u30d1\u30b9\u306e\u91dd\u3092\u523a\u3057\u3066\u5f27\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u3068\u304d\u30b3\u30f3\u30d1\u30b9\u304c\u63cf\u304f\u5f27\u304c\u5411\u304b\u3044\u5408\u3046\u8fba\u3068\u4ea4\u308f\u308b\u3088\u3046\u306b\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/span><\/p>\n\n\n\n \u5f27\u304c\u63cf\u3051\u305f\u3089\u3001\uff12\u3064\u306e\u4ea4\u70b9\u3092\u4ea4\u70b9\u30a2\u3001\u30a4\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n \u91dd\u306e\u5148\u3092\u4ea4\u70b9\u30a2\u306b\u7f6e\u304d\u63db\u3048\u3066\u3001\u5f27\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u4ea4\u70b9\u30a4\u3067\u3082\u540c\u3058\u3053\u3068\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n \u3059\u308b\u3068\u3001\uff12\u3064\u306e\u5f27\u304c\u4ea4\u308f\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u4ea4\u308f\u3063\u305f\u5f27\u306e\u4ea4\u70b9\u3068\u9802\u70b9\u3092\u7d50\u3076\u3088\u3046\u306b\u76f4\u7dda\u3092\u5f15\u304f\u3068\u3001\u3053\u308c\u304c\u5782\u76f4\u3067\u3059\u3002<\/p>\n\n\n \u540c\u69d8\u306b\u4ed6\u306e\u9802\u70b9\u304b\u3089\u3082\u5782\u7dda\u3092\u5f15\u3044\u3066\u3001\u4ea4\u308f\u3063\u305f\u70b9\u304c\u5782\u5fc3\u3067\u3059\u3002<\/p>\n\n\n \u5782\u5fc3\u306e\u5ea7\u6a19\u516c\u5f0f\u304c\u3042\u308b\u3053\u3068\u3092\u77e5\u3063\u3066\u3044\u307e\u3059\u304b\uff1f<\/p>\n\n\n\n \u4e0b\u306e\u56f3\u306e\u3088\u3046\u306a1\u8fba\u304c\\(y\\)\u8ef8\u306b\u5e73\u884c\u306a\u4e09\u89d2\u5f62\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n \u4e09\u89d2\u5f62\u306e\u5404\u9802\u70b9\u306e\u5ea7\u6a19\u3092\\(A(a_{x},a_{y}),B(0,0),C(c_{x},c_{y})\\)\u3068\u3059\u308b\u3002<\/p>\n\n\n\n \u3053\u306e\u3068\u304d\u5782\u5fc3H\u306e\u5ea7\u6a19\u306f<\/p>\n\n\n\n \\[\\displaystyle H(a_{x},\\frac{-a_{x}^{2}+a_{x}c_{x}+a_{y}c_{y}}{a_{y}})\\]<\/p>\n\n\n\n \u305f\u3060\u3057\u3001\u3053\u308c\u306f\u4e09\u89d2\u5f62\u306e1\u8fba\u304c\\(y\\)\u8ef8\u306b\u5e73\u884c\u304b\u30641\u3064\u306e\u9802\u70b9\u3092\u539f\u70b9\u3068\u3057\u305f\u3068\u304d\u306e\u5ea7\u6a19\u306a\u306e\u3067\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n \u4e09\u89d2\u5f62ABC\u306e\u5782\u5fc3\u3092H\u3068\u3059\u308b\u3068\u3001\u5782\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \\[\\displaystyle \\vec{h} =\\frac{\\tan A \\vec{a} + \\tan B \\vec{b} +\\tan C \\vec{c}}{\\tan A +\\tan B +\\tan C}\\]<\/p>\n\n\n\n \u3053\u308c\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u4e09\u89d2\u5f62\u3068\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u6027\u8cea\u304c\u95a2\u4fc2\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \u4e09\u89d2\u5f62ABC\u306b\u3064\u3044\u3066\u3001BC\u4e0a\u306e\u70b9P\u3001CA\u4e0a\u306e\u70b9Q\u3001AB\u4e0a\u306e\u70b9R\u306b\u5bfe\u3057\u3066<\/p>\n AR : RB = y : x \u306e\u3068\u304d\u3001\u7dda\u5206AP\u3001BQ\u3001CR\u306f\u30c1\u30a7\u30d0\u306e\u5b9a\u7406\u306b\u3088\u308a\u4e00\u70b9H\u3067\u4ea4\u308f\u308a\u3001H\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f<\/p>\n \\(\\displaystyle \\vec{h} =\\frac{x\\vec{a} + y\\vec{b} +z\\vec{c}}{x+y +z}\\)<\/p>\n \u3067\u8868\u3055\u308c\u308b\u3002<\/p>\n\n<\/div>\n\n\n\n \u3053\u306e\u6027\u8cea\u3092\u6d3b\u7528\u3057\u3066\u5782\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n \u4e0a\u306e\u56f3\u306e\u3088\u3046\u306b\u4e09\u89d2\u5f62ABC\u306e\u5782\u5fc3\u3092H\u3001AH\u3068BC\u306e\u4ea4\u70b9\u3092E\u3001BH\u3068CA\u306e\u4ea4\u70b9\u3092F\u3001CH\u3068AB\u306e\u4ea4\u70b9\u3092D\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u4e09\u89d2\u5f62AEB\u3068\u4e09\u89d2\u5f62AEC\u306f\u76f4\u89d2\u4e09\u89d2\u5f62\u306a\u306e\u3067\u3001<\/p>\n\n\n\n \\[AE = BE \\tan\u2061 B = EC \\tan\u2061 C\\]<\/p>\n\n\n\n \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u308c\u3092\u6bd4\u4f8b\u5f0f\u3068\u3057\u3066\u307f\u308b\u3068<\/p>\n\n\n\n \\[BE : EC = \\tan\u2061C : \\tan\u2061B\\]<\/p>\n\n\n\n \u3067\u3059\u3002<\/p>\n\n\n\n \u540c\u69d8\u306b<\/p>\n\n\n\n \\(AD : DB = \\tan \u2061B : \\tan A\\) \u3053\u3053\u3067\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u6027\u8cea\u3088\u308a\u5782\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f<\/p>\n\n\n\n \\[\\displaystyle \\vec{h} =\\frac{\\tan A \\vec{a} + \\tan B \\vec{b} +\\tan C \\vec{c}}{\\tan A +\\tan B +\\tan C}\\]<\/p>\n\n\n\n \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u5782\u5fc3\u306e\u4ed6\u306b\u3082\u300c\u5185\u5fc3\u300d<\/span>\u3084\u300c\u91cd\u5fc3\u300d<\/span>\u306a\u3069\u4e94\u5fc3\u306b\u306f\u91cd\u8981\u306a\u70b9\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u4eca\u56de\u306f\u4e94\u5fc3\u306e\u4e2d\u304b\u3089\u300c\u5782\u5fc3\u300d<\/span>\u3092\u30d4\u30c3\u30af\u30a2\u30c3\u30d7\u3057\u3066\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u3068\u306f\u3001\u5404\u9802\u70b9\u304b\u3089\u5bfe\u8fba\u306b\u5411\u304b\u3063\u3066\u3072\u3044\u305f\u5782\u7dda\u306e\u4ea4\u70b9<\/span>\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u5782\u5fc3\u306e\u6027\u8cea<\/p>\n \u5782\u5fc3\u306e\u6027\u8cea\u306f\u77e5\u3063\u3066\u3044\u308b\u3082\u306e\u3068\u3057\u3066\u554f\u984c\u304c\u51fa\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n \u5782\u7dda\u304c\uff11\u70b9\u3067\u4ea4\u308f\u308b\u3053\u3068\u306e\u8a3c\u660e\u306b\u306f\u4ed6\u306e\u65b9\u6cd5\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u305f\u3060\u3001\u4eca\u56de\u7d39\u4ecb\u3057\u305f\u8a3c\u660e\u304c1\u756a\u308f\u304b\u308a\u3084\u3059\u3044\u3068\u611f\u3058\u305f\u306e\u3067\u78ba\u8a8d\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u5782\u5fc3\u306e\u4ed6\u306b\u3082\u300c\u5185\u5fc3\u300d<\/span>\u3084\u300c\u91cd\u5fc3\u300d<\/span>\u306a\u3069\u4e94\u5fc3\u306b\u306f\u91cd\u8981\u306a\u70b9\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u304c\u3044\u307e\u3044\u3061\u306a\u65b9\u306f\u5fc5\u898b\u3067\u3059\uff01 \u4eca\u56de\u306f\u5782\u5fc3\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u500b\u5225\u6307\u5c0e\u6b7410\u5e74\u306e\u6570\u5b66\u8b1b\u5e2b\u304c\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u4e09\u89d2\u5f62\u306b\u306f\u4e94\u5fc3\u3068\u547c\u3070\u308c\u308b5\u3064\u306e\u70b9\u304c\u3042\u308a\u307e\u3059\u3002 \u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u3068\u306f\u3001\u5404\u9802\u70b9\u304b\u3089\u5bfe\u8fba\u306b\u5411\u304b\u3063\u3066\u5782\u7dda\u3092\u5f15\u3044\u305f\u4ea4\u70b9\u3092\u6307 […]<\/p>\n","protected":false},"author":1,"featured_media":4905,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[29,223],"tags":[28,10,11],"class_list":["post-1714","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>
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n\u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u3068\u306f\uff1f<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
\u5404\u9802\u70b9\u304b\u3089\u5411\u304b\u3044\u5408\u3046\u8fba\u306b\u4e0b\u3057\u305f\u5782\u7dda\u306e\u4ea4\u70b9<\/span><\/div>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>\u5782\u7dda\u304c1\u70b9\u3067\u4ea4\u308f\u308b\u3053\u3068\u306e\u8a3c\u660e<\/h3>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
\\angle \\mathrm{ADC} &=&180^{\\circ}-\\angle \\mathrm{DAC}-\\angle \\mathrm{ACD} \\\\
&=&180^{\\circ}-\\angle \\mathrm{BAF}-\\angle \\mathrm{ABF} \\\\
&=&\\angle \\mathrm{AFB} \\\\
&=&90^{\\circ}
\\end{eqnarray}<\/p>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\u5782\u5fc3\u304c\u6301\u3064\u6027\u8cea<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
R\u306f\u4e09\u89d2\u5f62ABC\u306e\u5916\u63a5\u5186\u306e\u534a\u5f84\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n
<\/figure>\n<\/div>\n\n\n\u5782\u5fc3\u306e\u6027\u8cea\u300a\u8a3c\u660e\u300b<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n\u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u306e\u898b\u3064\u3051\u65b9<\/h2>\n\n\n
<\/figure>\n<\/div>\n\n\n\n
\u5782\u5fc3\u306e\u4f5c\u56f3<\/h3>\n\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\u5782\u5fc3\u306e\u5ea7\u6a19<\/h3>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\u5782\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/h3>\n\n\n\n
BP : PC = z : y
CQ : QA = x : z<\/p>\n
<\/figure>\n<\/div>\n\n\n
\\(CF : FA = \\tan \u2061A : \\tan \u2061C\\)<\/p>\n\n\n\n\u4e09\u89d2\u5f62\u306e\u5782\u5fc3\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\n \t