{"id":1651,"date":"2025-12-24T17:19:57","date_gmt":"2025-12-24T08:19:57","guid":{"rendered":"https:\/\/math-travel.com\/?p=1651"},"modified":"2026-02-11T16:42:16","modified_gmt":"2026-02-11T07:42:16","slug":"incenter","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-a\/incenter\/","title":{"rendered":"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3068\u306f\uff1f\u6027\u8cea\u30fb\u610f\u5473\u30fb\u5ea7\u6a19\u3068\u30d9\u30af\u30c8\u30eb\u306e\u6c42\u3081\u65b9\u3092\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"\n

\u300c\u5185\u5fc3\u3063\u3066\u3069\u3093\u306a\u70b9\u3060\u3063\u3051\u300d<\/span>
\u300c\u5185\u5fc3\u306e\u6027\u8cea\u304c\u77e5\u308a\u305f\u3044\u300d<\/span><\/p>\n\n\n\n

\u4eca\u56de\u306f\u5185\u5fc3\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u5185\u5fc3\u306e\u5b9a\u7fa9\u3084\u6027\u8cea\u304c\u77e5\u308a\u305f\u304f\u3066\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u4e09\u89d2\u5f62\u306b\u306f\u4e94\u5fc3\u3068\u3044\u30465\u3064\u306e\u70b9<\/span>\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u4e09\u89d2\u5f62\u306e\u4e94\u5fc3\u306e\u4e00\u89a7\"<\/figure>\n<\/div>\n\n\n

\u4e94\u5fc3\u306e\u4e2d\u3067\u3082\u300c\u5185\u5fc3<\/span>\u300d\u3084\u300c\u91cd\u5fc3<\/span>\u300d\u306f\u3088\u304f\u51fa\u984c\u3055\u308c\u308b\u91cd\u8981\u306a\u70b9\u3067\u3059\u306d\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3068\u306f\u3001\u300c\u4e09\u89d2\u5f62\u306e3\u3064\u306e\u5185\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u306e\u4ea4\u70b9<\/span>\u300d\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\"<\/figure>\n<\/div>\n\n\n

\u307e\u305f\u5185\u5fc3\u306e\u5ea7\u6a19\u3084\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u305f\u3060\u3057\u3001\u516c\u5f0f\u306b\u4ee3\u5165\u3057\u305f\u3060\u3051\u3067\u306f\u6e1b\u70b9\u5bfe\u8c61<\/span>\u306a\u306e\u3067\u8a18\u8ff0\u554f\u984c\u306e\u691c\u7b97\u306b\u6d3b\u7528\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u300a\u5185\u5fc3\u306e\u5ea7\u6a19\u516c\u5f0f\u300b<\/span><\/p>\n\n\n

\n
\"\u5185\u5fc3\u306e\u5ea7\u6a19\u516c\u5f0f\"<\/figure>\n<\/div>\n\n\n

\\(\\triangle ABC\\)\u306b\u304a\u3044\u3066\u3001\\(A(x_{a},y_{a}),B(x_{b},y_{b}),C(x_{c},y_{c})\\)\u3068\u3059\u308b\u3068\u5185\u5fc3\\(I\\)\u306e\u5ea7\u6a19\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

\\[\\displaystyle I \\left(\\frac{ax_{a}+bx_{b}+cx_{c}}{a+b+c},\\frac{ay_{a}+by_{b}+cy_{c}}{a+b+c}\\right)\\]<\/p>\n\n\n\n

\u300a\u5185\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u300b<\/span>
\\(\\triangle ABC\\)\u306b\u304a\u3044\u3066\u3001\\(A(\\vec{a}),B(\\vec{b}),C(\\vec{c})\\)\u3068\u3059\u308b\u3068\u5185\u5fc3\\(I\\)\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\\(\\vec{i}\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

[\\displaystyle \\vec{i}=\\frac{a \\vec{a}+b \\vec{b}+c \\vec{c}}{a+b+c}]<\/p>\n\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f\u3001\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306e\u5b9a\u7fa9\u3084\u6027\u8cea\u306a\u3069\u3092\u89e3\u8aac<\/span>\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u5185\u5fc3\u306b\u95a2\u3059\u308b\u7591\u554f\u304c\u3042\u308b\u65b9\u306f\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3068\u306f<\/h2>\n\n\n\n

\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3068\u306f\u3001\u4e09\u89d2\u5f62\u306e3\u3064\u306e\u5185\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u306e\u4ea4\u70b9<\/span>\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u4f8b\u3048\u3070\u3053\u306e\u70b9\u3067\u3059\u3002<\/p>\n\n\n

\n
\"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3068\u306f\"<\/figure>\n<\/div>\n\n\n

\u3053\u306e\u70b9\u3001\u9069\u5f53\u306b\u63cf\u3044\u305f\u70b9\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n

\n
\"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3068\u306f\"<\/figure>\n<\/div>\n\n\n

\u5404\u89d2\u306e2\u7b49\u5206\u7dda\u3092\u5f15\u3044\u305f\u7d50\u679c\u3001\u4ea4\u308f\u3063\u305f\u4ea4\u70b9\u306a\u306e\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

\u3053\u308c\u304c\u3001\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3067\u3059\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u5f62\u306e\u5185\u5074\u306b\u63a5\u3059\u308b\u5186\u306e\u3053\u3068\u3092\u300c\u5185\u63a5\u5186\u300d<\/span>\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n

\u5185\u5fc3\u306b\u306f\u300c\u5185\u63a5\u5186\u306e\u4e2d\u5fc3\u3067\u3042\u308b<\/span>\u300d\u3068\u3044\u3046\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u5185\u63a5\u5186\u306e\u4e2d\u5fc3\"<\/figure>\n<\/div>\n\n\n

\u3053\u306e\u3042\u3068\u5185\u5fc3\u306e\u6027\u8cea\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u5185\u5fc3\u3068\u5916\u5fc3\u306e\u9055\u3044<\/h2>\n\n\n\n

“\u5185\u5fc3”\u3068”\u5916\u5fc3”\u306f\u3088\u304f\u51fa\u3066\u304f\u308b\u70b9\u306a\u306e\u3067\u3001\u9055\u3044\u3092\u7406\u89e3\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u5185\u5fc3\u306f\u4e09\u89d2\u5f62\u306e\u5185\u63a5\u5186\u306e\u4e2d\u5fc3\u3067\u3059\u304c\u3001\u5916\u5fc3\u306f\u5916\u63a5\u5186\u306e\u4e2d\u5fc3\u3068\u306a\u308b\u70b9\u3067\u3059\u3002<\/p>\n\n\n

\n
\"\u4e09\u89d2\u5f62\u306e\u5916\u63a5\u5186\"<\/figure>\n<\/div>\n\n\n

\u307e\u305f\u3001\u5916\u5fc3\u306f\u5404\u8fba\u306e\u5782\u76f4\u4e8c\u7b49\u5206\u7dda\u306e\u4ea4\u70b9\u3067\u3059\u3002<\/p>\n\n\n

\n
\"\u4e09\u89d2\u5f62\u306e\u5916\u5fc3\u306e\u5b9a\u7fa9\"<\/figure>\n<\/div>\n\n\n

\u5185\u5fc3\u3068\u5916\u5fc3\u306e\u6027\u8cea\u3092\u7c21\u5358\u306b\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u5185\u5fc3<\/span><\/th>\u5916\u5fc3<\/span><\/th><\/tr><\/thead>
\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u306e\u4ea4\u70b9<\/th>\u5782\u76f4\u4e8c\u7b49\u5206\u7dda\u306e\u4ea4\u70b9<\/td><\/tr>
\u5185\u63a5\u5186\u306e\u4e2d\u5fc3<\/th>\u5916\u63a5\u5186\u306e\u4e2d\u5fc3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u5916\u5fc3\u306b\u3064\u3044\u3066\u306f\u300c\u5916\u5fc3\u306e\u6027\u8cea\u3068\u8a3c\u660e\u300d\u3067\u8a73\u3057\u304f\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u5916\u5fc3\u306f\u4e2d\u7dda\u306e\u4ea4\u70b9\u306a\u3093\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u305d\u3046\u306a\u3093\u3060\u3088\uff01\u5916\u5fc3\u3082\u4e00\u7dd2\u306b\u7406\u89e3\u3057\u3066\u304a\u3053\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u5185\u5fc3\u306e\u5ea7\u6a19\u516c\u5f0f<\/h2>\n\n\n\n

\u305d\u308c\u3067\u306f\u5185\u5fc3\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

\u307e\u305a\u306f\u5185\u5fc3\u306e\u5ea7\u6a19\u516c\u5f0f<\/span>\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u5ea7\u6a19\u516c\u5f0f<\/h3>\n\n\n
\n
\"\u5185\u5fc3\u306e\u5ea7\u6a19\u516c\u5f0f\"<\/figure>\n<\/div>\n\n\n

\\(\\triangle ABC\\)\u306b\u304a\u3044\u3066\u3001\\(BC=a,AC=b,AB=c,A(x_{a},y_{a}),B(x_{b},y_{b}),C(x_{c},y_{c})\\)\u3068\u3059\u308b\u3068\u5185\u5fc3\\(I\\)\u306e\u5ea7\u6a19\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3067\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

[\\displaystyle I \\left(\\frac{ax_{a}+bx_{b}+cx_{c}}{a+b+c},\\frac{ay_{a}+by_{b}+cy_{c}}{a+b+c}\\right)]\u3044<\/p>\n\n\n\n

\u305f\u3060\u3057\u3001\u516c\u5f0f\u306b\u6570\u5b57\u3092\u4ee3\u5165\u3057\u305f\u3060\u3051\u3067\u306f\u6e1b\u70b9\u5bfe\u8c61<\/span>\u306a\u306e\u3067\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u8a18\u8ff0\u554f\u984c\u306e\u3068\u304d\u306f\u3001\u9014\u4e2d\u5f0f\u3082\u3057\u3063\u304b\u308a\u66f8\u3053\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u5185\u5fc3\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u308b<\/h3>\n\n\n\n

\\(\\triangle ABC\\)\u306b\u304a\u3044\u3066\u3001\u5404\u9802\u70b9\u306e\u5ea7\u6a19\u3092\\(A(3,4),B(0,0),C(7,0)\\)\u3068\u3059\u308b\u3002<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

\u3053\u306e\u3068\u304d\u4e09\u89d2\u5f62\u306e\u5404\u8fba\u306e\u9577\u3055\u306f<\/p>\n\n\n\n

\\(BC=7\\)<\/p>\n\n\n\n

\\(AC=\\sqrt{(7-3)^{2}+4^{2}}=4\\sqrt{2}\\)<\/p>\n\n\n\n

\\(AB=\\sqrt{3^{2}+4^{2}=5}\\)<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001\u5185\u5fc3\u306e\u516c\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068<\/p>\n\n\n\n

\\[\\displaystyle I \\left(\\frac{7 \\cdot 3+4\\sqrt{2} \\cdot 0+5 \\cdot7}{7+ 4\\sqrt{2} +5},\\frac{7 \\cdot 4+4\\sqrt{2} \\cdot 0+5 \\cdot0}{7+ 4\\sqrt{2} +5}\\right)\\]<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

\\[\\displaystyle I \\left(\\frac{14}{3+\\sqrt{2}},\\frac{7}{3+\\sqrt{2}}\\right)\\]<\/p>\n\n\n\n

\u3053\u308c\u3067\u5185\u5fc3\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u5ea7\u6a19\u516c\u5f0f\u306e\u8a3c\u660e<\/h3>\n\n\n\n

\u5185\u5fc3\\(I\\)\u306e\u5ea7\u6a19\u516c\u5f0f\u306e\u8a3c\u660e\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u5185\u5fc3\u306e\u8a3c\u660e\u306b\u306f\u3001\u5185\u5206\u70b9\u306e\u516c\u5f0f\u3092\u6d3b\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\\(\\triangle ABC\\)\u306b\u304a\u3044\u3066\u3001\\(BC=a,AC=b,AB=c,A(x_{a},y_{a}),B(x_{b},y_{b}),C(x_{c},y_{c})\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n

\n
\"\u5ea7\u6a19\u516c\u5f0f\u306e\u8a3c\u660e\"<\/figure>\n<\/div>\n\n\n

\u89d2C\u306e\u4e8c\u7b49\u5206\u7dda\u3068\u8fbaAB\u3068\u306e\u4ea4\u70b9\u3092\u70b9D\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n

\\[AD:DB=CA:CB=b:a\\]<\/p>\n\n\n

\n
\"\u5ea7\u6a19\u516c\u5f0f\u306e\u8a3c\u660e\"<\/figure>\n<\/div>\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

\\[\\displaystyle D \\left(\\frac{ax_{a}+bx_{b}}{b+a},\\frac{ay_{a}+by_{b}}{b+a}\\right)\\]<\/p>\n\n\n\n

\u307e\u305f\u3001\\(AD:DB=b:a\\)\u3088\u308a<\/p>\n\n\n\n

\\[\\displaystyle AD=\\frac{b}{a+b} AB=\\frac{b}{a+b} c\\]<\/p>\n\n\n

\n
\"\u5ea7\u6a19\u516c\u5f0f\u306e\u8a3c\u660e2\"<\/figure>\n<\/div>\n\n\n

\u3064\u304e\u306b<\/p>\n\n\n\n

\\[\\displaystyle CI:ID=AC:AD=b:\\frac{b}{a+b}c=(a+b):c\\]<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

\\[\\displaystyle I\\left(\\frac{(a+b) \\cdot \\frac{ax_{a}+bx_{b}}{b+a}+cx_{c}}{(a+b)+c},\\frac{(a+b) \\cdot \\frac{ay_{a}+by_{b}}{b+a}+cy_{c}}{(a+b)+c}\\right)\\]<\/p>\n\n\n\n

\u3068\u306a\u308a\u3001\u5185\u5fc3\u306e\u5ea7\u6a19\u516c\u5f0f\u306f<\/p>\n\n\n\n

[\\displaystyle I(\\frac{ax_{a}+bx_{b}+cx_{c}}{a+b+c},\\frac{ay_{a}+by_{b}+cy_{c}}{a+b+c})]<\/p>\n\n\n\n

\u5185\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/h2>\n\n\n\n

\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/h3>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n

\\(\\triangle ABC\\)\u306b\u304a\u3044\u3066\u3001\\(A(\\vec{a}),B(\\vec{b}),C(\\vec{c})\\)\u3068\u3059\u308b\u3068\u5185\u5fc3I\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\\[\\displaystyle \\vec{i}=\\frac{a \\vec{a}+b \\vec{b}+c \\vec{c}}{a+b+c}\\]<\/p>\n\n\n\n

\u5185\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u308b<\/h3>\n\n\n\n

\\(\\triangle ABC\\)\u306b\u304a\u3044\u3066\u3001\\(A(\\vec{a})=(3,4),B(\\vec{b})=(0,0),C(\\vec{c})=(7,0)\\)\u3068\u3059\u308b\u3002<\/p>\n\n\n\n

\u3053\u306e\u3068\u304d\u4e09\u89d2\u5f62\u306e\u5404\u8fba\u306e\u9577\u3055\u306f<\/p>\n\n\n\n

\\(BC=7\\)<\/p>\n\n\n\n

\\(AC=\\sqrt{(7-3)^{2}+4^{2}}=4\\sqrt{2}\\)<\/p>\n\n\n\n

\\(AB=\\sqrt{3^{2}+4^{2}=5}\\)<\/p>\n\n\n\n

\u3086\u3048\u306b\u5185\u5fc3\\(I(\\vec{i})\\)\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f<\/p>\n\n\n\n

\\[\\displaystyle \\vec{i}=\\frac{7 \\vec{a}+4\\sqrt{2} \\vec{b}+5 \\vec{c}}{7+ 4\\sqrt{2} +5}\\]<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

\\begin{eqnarray}
\\displaystyle \\vec{i}&=&\\frac{7(3,4)+4(0,0)+5(7,0)}{12+ 4\\sqrt{2}}\\\\
\\displaystyle &=&\\frac{(56,28)}{12+ 4\\sqrt{2}}\\\\
\\displaystyle &=&\\frac{(14,7)}{3+ \\sqrt{2}}
\\end{eqnarray}<\/p>\n\n\n\n

\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u8a3c\u660e<\/h3>\n\n\n\n

\u5185\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306e\u516c\u5f0f\u3092\u6c42\u3081\u308b\u306b\u3042\u305f\u3063\u3066\u5fc5\u8981\u306a\u516c\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u5185\u5fc3\u306e\u6027\u8cea\u304b\u3089\u9762\u7a4d\u6bd4\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

\\(\\triangle \\mathrm{ABC}\\)\u306e\u5185\u63a5\u5186\u306e\u534a\u5f84\u3092r\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n

\n
\"\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u8a3c\u660e\"<\/figure>\n<\/div>\n\n\n

\u9762\u7a4d\u6bd4 \\(\\displaystyle \\triangle \\mathrm{IBC}: \\triangle \\mathrm{ICA}: \\triangle \\mathrm{IAB}=\\frac{1}{2} a r: \\frac{1}{2} b r: \\frac{1}{2} \\mathrm{cr}=a: b: c\\)<\/p>\n\n\n\n

\u3053\u3053\u3067\u5148\u307b\u3069\u78ba\u8a8d\u3057\u305f\u9762\u7a4d\u6bd4\u306e\u516c\u5f0f\u3092\u6d3b\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\\[\\displaystyle \\triangle \\mathrm{IBC}: \\triangle \\mathrm{ICA}: \\triangle \\mathrm{IAB}=a: b: c\\]<\/p>\n\n\n\n

\u306a\u306e\u3067\u3001<\/p>\n\n\n\n

\\[\\displaystyle \\vec{i}=\\frac{a \\vec{a}+b \\vec{b}+c \\vec{c}}{a+b+c}\\]<\/p>\n\n\n\n

\u3088\u3063\u3066\u3001\u8a3c\u660e\u5b8c\u4e86\u3067\u3059\u3002<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u96e3\u3057\u304f\u3066\u3088\u304f\u5206\u304b\u3089\u306a\u304b\u3063\u305f\u3067\u3059\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u5206\u304b\u3089\u306a\u304b\u3063\u305f\u3089\u98db\u3070\u3057\u3066\u5927\u4e08\u592b\u3060\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u6027\u8cea\u300b<\/h2>\n\n\n
\n
\"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u6027\u8cea\u300b\"<\/figure>\n<\/div>\n\n\n

\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306b\u306f\u3044\u304f\u3064\u304b\u306e\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

    \n
  1. \u89d2\u3092\u4e8c\u7b49\u5206\u3059\u308b<\/li>\n\n\n\n
  2. \u5185\u5fc3\u304b\u3089\u5404\u8fba\u307e\u3067\u306e\u8ddd\u96e2\u304c\u7b49\u3057\u3044<\/li>\n\n\n\n
  3. \u5185\u63a5\u5186\u306e\u4e2d\u5fc3<\/li>\n<\/ol>\n\n\n\n

    \uff11\uff1a\u89d2\u3092\u4e8c\u7b49\u5206\u3059\u308b<\/span><\/p>\n\n\n\n

    \u5185\u5fc3\u306e\u5b9a\u7fa9\u304c\u300c\u5185\u89d2\u306e\u4e8c\u7b49\u5206\u306e\u4ea4\u70b9\u300d\u306a\u306e\u3067\u3059\u3050\u306b\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u6027\u8cea\u300b\"<\/figure>\n<\/div>\n\n\n

    \uff12\uff1a\u5185\u5fc3\u304b\u3089\u5404\u8fba\u307e\u3067\u306e\u8ddd\u96e2\u304c\u7b49\u3057\u3044<\/span><\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u6027\u8cea\u300b\"<\/figure>\n<\/div>\n\n\n

    \uff13\uff1a\u5185\u63a5\u5186\u306e\u4e2d\u5fc3<\/span><\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u6027\u8cea\u300b\"<\/figure>\n<\/div>\n\n\n

    \uff12\u306e\u5fdc\u7528\u306b\u306a\u308a\u307e\u3059\u304c\u3001\u5404\u8fba\u307e\u3067\u306e\u8ddd\u96e2\u304c\u7b49\u3057\u3044\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u305d\u3053\u306b\u5186\u304c\u66f8\u3051\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n\n\n\n

    \u3057\u305f\u304c\u3063\u3066\u3001\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306f\u5185\u63a5\u5186\u306e\u4e2d\u5fc3\u3067\u3082\u3042\u308b\u306e\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

    \u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u8a3c\u660e\u300b<\/h3>\n\n\n
    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u8a3c\u660e\u300b\"<\/figure>\n<\/div>\n\n\n

    \u3067\u306f\u3001\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u304c\u6301\u3064\u6027\u8cea\u306e\u8a3c\u660e\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

    \uff11\u306e\u300c\u89d2\u3092\u4e8c\u7b49\u5206\u3059\u308b\u300d\u306f\u5b9a\u7fa9\u306a\u306e\u3067\u3001\u305d\u3046\u3044\u3046\u3082\u306e\u3060\u3068\u601d\u3063\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

    \uff12\u306e\u300c\u5185\u5fc3\u304b\u3089\u5404\u8fba\u307e\u3067\u306e\u8ddd\u96e2\u304c\u7b49\u3057\u3044\u300d\u304c\u8a3c\u660e\u3067\u304d\u308c\u3070\u3001\uff13\u306e\u300c\u5185\u63a5\u5186\u306e\u4e2d\u5fc3\u300d\u3067\u3042\u308b\u3053\u3068\u306f\u5186\u3092\u66f8\u3051\u3070\u898b\u3048\u3066\u304d\u307e\u3059\u306d\u3002<\/p>\n\n\n\n

    \u305d\u308c\u3067\u306f\u3001\u5185\u5fc3\u304b\u3089\u5404\u8fba\u307e\u3067\u306e\u8ddd\u96e2\u304c\u7b49\u3057\u304f\u306a\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

    \u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u4e0a\u306b\u70b9\u3092\u3068\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

    \u70b9\u3068\u8fba\u306e\u8ddd\u96e2\u306f\u5782\u76f4\u306b\u4ea4\u308f\u308b\u6700\u77ed\u306e\u7dda\u5206\u306a\u306e\u3067\u3001\u89d2\u3092\u5206\u3051\u3089\u308c\u305f\u4e8c\u8fba\u306b\u5782\u7dda\u3092\u5f15\u304f\u3053\u3068\u3067\u3001\uff12\u3064\u306e\u76f4\u89d2\u4e09\u89d2\u5f62\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

    \uff12\u3064\u306e\u76f4\u89d2\u4e09\u89d2\u5f62\u306f\u3001\u659c\u8fba\u3092\u5171\u6709\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u659c\u8fba\u3068\uff11\u3064\u306e\u92ed\u89d2\u304c\u305d\u308c\u305e\u308c\u7b49\u3057\u3044\u306e\u3067\u3001\u5408\u540c\u306a\u76f4\u89d2\u4e09\u89d2\u5f62\u3068\u3044\u3048\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u8a3c\u660e\u300b\"<\/figure>\n<\/div>\n\n\n

    \u307e\u305f\u3001\u540c\u3058\u3053\u3068\u3092\u5225\u306e\u4e09\u89d2\u5f62\u3067\u3082\u884c\u3046\u3053\u3068\u3067\u3001\u3053\u3061\u3089\u3067\u3082\u70b9\u304b\u3089\u8fba\u307e\u3067\u306e\u8ddd\u96e2\u304c\u7b49\u3057\u304f\u306a\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u8a3c\u660e\u300b\"<\/figure>\n<\/div>\n\n\n

    \u3057\u305f\u304c\u3063\u3066\u3001\u5404\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u306e\u4ea4\u70b9\u3067\u3042\u308b\u5185\u5fc3\u306f\u3001\u5404\u8fba\u307e\u3067\u306e\u8ddd\u96e2\u304c\u7b49\u3057\u3044\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u8a3c\u660e\u300b\"<\/figure>\n<\/div>\n\n\n

    \u3057\u305f\u304c\u3063\u3066\u3001\u5404\u8fba\u307e\u3067\u306e\u5782\u7dda\u3092\u534a\u5f84\u3068\u898b\u305f\u3068\u304d\u3001\u5185\u63a5\u5186\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u3001\u5185\u5fc3\u306f\u5185\u63a5\u5186\u306e\u4e2d\u5fc3\u3067\u3042\u308b\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u300a\u8a3c\u660e\u300b\"<\/figure>\n<\/div>\n\n\n

    \u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306e\u898b\u3064\u3051\u65b9<\/h2>\n\n\n\n

    \u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306f\u3001\u5b9f\u969b\u306b\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u3092\u5f15\u304f\u3053\u3068\u3067\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

    \u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u306e\u5f15\u304d\u65b9\u306f\u4e2d\u5b66\u6821\u3067\u3082\u7fd2\u3044\u307e\u3057\u305f\u306d\u3002<\/p>\n\n\n

    \n
    \"\u5185\u5fc3\u306e\u4f5c\u56f3\u306b\u5fc5\u8981\u306a\u3082\u306e\"<\/figure>\n<\/div>\n\n\n

    \u307e\u305a\u597d\u304d\u306a\u9802\u70b9\u304b\u3089\u3001\u5f27\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

    \u3059\u308b\u3068\u3001\uff12\u3064\u306e\u8fba\u306e\u4ea4\u308f\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306e\u898b\u3064\u3051\u65b9""\"<\/figure>\n<\/div>\n\n\n

    \u305d\u306e\u4ea4\u70b9\u3092\u4ea4\u70b9\u30a2\u3001\u30a4\u3068\u3067\u3082\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

    \u3064\u304e\u306f\u4ea4\u70b9\u30a2\u306b\u91dd\u3092\u7f6e\u304d\u306a\u304a\u3057\u3001\u518d\u5ea6\u4e09\u89d2\u5f62\u306e\u5185\u5074\u306b\u5f27\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306e\u898b\u3064\u3051\u65b9\"<\/figure>\n<\/div>\n\n\n

    \u3053\u308c\u3092\u4ea4\u70b9\u30a4\u3067\u3082\u884c\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

    \u3059\u308b\u3068\u3001\u304a\u4e92\u3044\u306e\u5f27\u304c\u4ea4\u308f\u308b\u306e\u3067\u3001\u521d\u3081\u306b\u9078\u3093\u3060\u9802\u70b9\u304b\u3089\u7dda\u3092\u5f15\u304f\u3068\u3001\u305d\u308c\u304c\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u3067\u3059\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306e\u898b\u3064\u3051\u65b9\"<\/figure>\n<\/div>\n\n\n

    \u540c\u3058\u3053\u3068\u3092\u5225\u306e\u9802\u70b9\u3067\u3082\u884c\u3044\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306e\u898b\u3064\u3051\u65b9\"<\/figure>\n<\/div>\n\n\n

    \u3059\u308b\u3068\u3001\u4e00\u304b\u6240\u3067\u4ea4\u308f\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

    \u3053\u308c\u304c\u3001\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3067\u3059\u3002<\/p>\n\n\n\n

    \u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n

    \u4eca\u56de\u306f\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n

    \n
    \"\u4e09\u89d2\u5f62\u306e\u5185\u5fc3\"<\/figure>\n<\/div>\n\n\n

    \u4e09\u89d2\u5f62\u306e\u5185\u5fc3\u306f\u3088\u304f\u51fa\u3066\u304f\u308b\u70b9\u306a\u306e\u3067\u3001\u6027\u8cea\u3082\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

    \u5185\u5fc3\u306e\u5b9a\u7fa9\u3084\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

    \u4eca\u56de\u306f\u4e94\u5fc3\u306e\u306a\u304b\u304b\u3089”\u5185\u5fc3”\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

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