<\/figure>\n<\/div>\n\n\n\u508d\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/h2>\n\n\n\n
3\u70b9\u306e\u508d\u5fc3\\(I_{a},I_{b},I_{c}\\)\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n
\u508d\u5fc3\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u300a\u8a3c\u660e\u300b<\/h3>\n\n\n\n
\u8fba \\(BC\\) \u306b\u95a2\u3057\u3066\u9802\u70b9\\(A\\)\u3068\u53cd\u8a0e\u5074\u306b\u3042\u308b\u508d\u5fc3\\(I_{a}\\left(\\vec{i_{a}}\\right)\\)\u306b\u3064\u3044\u3066\u8a3c\u660e\u3057\u307e\u3059\u3002
\uff08\u4ed6\u306e\u508d\u5fc3\u306e\u5834\u5408\u3082\u540c\u6a23)<\/p>\n\n\n\n
\\(I_{a}\\)\u306f\u89d2\\(A\\)\u306e2\u7b49\u5206\u7dda\u4e0a\u306b\u3042\u308b\u304b\u3089<\/p>\n\n\n\n
\\[\\displaystyle \\overrightarrow{AI_{a}}=s\\left(\\frac{1}{c} \\overrightarrow{\\mathrm{AB}}+\\frac{1}{b} \\overrightarrow{\\mathrm{AC}}\\right)(0<s) \\]<\/p>\n\n\n\n
\u3068\u8868\u305b\u308b\u3002<\/p>\n\n\n\n
\u4e00\u65b9\u3067\u3001<\/p>\n\n\n\n
\\(\\mathrm{I}_{a}\\)\u306f\u89d2\\(C\\)\u306e\u5916\u89d2\u306e2\u7b49\u5206\u7dda\u4e0a\u306e\u70b9\u3067\u3082\u3042\u308b\u304b\u3089<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle \\overrightarrow{AI_{a}}&=&\\overrightarrow{AC}+\\overrightarrow{CI_{a}}\\\\
\\displaystyle &=&\\overrightarrow{AC}+t\\left(\\frac{1}{a} \\overrightarrow{CB}+\\frac{1}{b} \\overrightarrow{AC}\\right) \\quad(t>0)\\\\
\\displaystyle &=&\\overrightarrow{AC}+t\\left\\{\\frac{1}{a}(\\overrightarrow{AB}-\\overrightarrow{AC})+\\frac{1}{b} \\overrightarrow{AC}\\right\\}\\\\
\\displaystyle &=&\\frac{t}{a} \\overrightarrow{AB}+\\left(1-\\frac{t}{a}+\\frac{t}{b}\\right) \\overrightarrow{AC}
\\end{eqnarray}<\/p>\n\n\n\n
\u3068\u8868\u3059\u3053\u3068\u3082\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\\(\\overrightarrow{\\mathrm{AB}} \\neq \\overrightarrow{0}, \\overrightarrow{\\mathrm{AC}} \\neq \\overrightarrow{0} \\)\u304b\u3064\\(\\overrightarrow{\\mathrm{AB}}\\)\u3068\\(\\overrightarrow{\\mathrm{AC}}\\)\u306f\u5e73\u884c\u3067\u306a\u3044\u306e\u3067,<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle \\frac{s}{c}&=&\\frac{t}{a}\\\\
\\displaystyle \\frac{s}{b}&=&1-\\frac{t}{a}+\\frac{t}{b}
\\end{eqnarray}<\/p>\n\n\n\n
\u3092\u5f97\u308b\u3002<\/p>\n\n\n\n
\u3053\u308c\u3092\u89e3\u3044\u3066\u3001<\/p>\n\n\n\n
\\[\\displaystyle s=\\frac{b c}{-a+b+c}, \\quad t=\\frac{a b}{-a+b+c}\\]<\/p>\n\n\n\n
\u3088\u3063\u3066\u3001<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle \\overrightarrow{\\mathrm{AI_{a}}}&=&\\frac{b}{-a+b+c} \\overrightarrow{\\mathrm{AB}}+\\frac{c}{-a+b+c} \\overrightarrow{\\mathrm{AC}}\\\\
\\displaystyle &=&\\frac{b}{-a+b+c}(\\vec{b}-\\vec{a})+\\frac{c}{-a+b+c}(\\vec{c}-\\vec{a})\\\\
\\displaystyle &=&\\frac{-b-c}{-a+b+c} \\vec{a}+\\frac{b}{-a+b+c} \\vec{b}+\\frac{c}{-a+b+c} \\vec{c}
\\end{eqnarray}<\/p>\n\n\n\n
\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n
\\begin{eqnarray}
\\displaystyle \\vec{i_{a}}&=&\\vec{a}+\\overrightarrow{\\mathrm{AI_{a}}}\\\\
\\displaystyle &=&\\frac{-a \\vec{a}+b \\vec{b}+c \\vec{c}}{-a+b+c}
\\end{eqnarray}<\/p>\n\n\n\n
\u3088\u3063\u3066\u8a3c\u660e\u7d42\u4e86<\/p>\n\n\n\n
\u4e09\u89d2\u5f62\u306e\u508d\u5fc3\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n
\u4eca\u56de\u306f\u508d\u5fc3\u306e\u5b9a\u7fa9\u3084\u6027\u8cea\u3092\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n
\n
<\/figure>\n<\/div>\n\n\n\u21d2\u508d\u5fc3\u306e\u6027\u8cea\u306b\u3064\u3044\u3066<\/a>\u306f\u3053\u3061\u3089<\/p>\n\n\n\n\u508d\u5fc3\u306f\u306a\u304b\u306a\u304b\u554f\u984c\u306b\u51fa\u3066\u304d\u307e\u305b\u3093\u304c\u3001\u77e5\u3063\u3066\u304a\u304f\u3068\u5468\u308a\u3068\u5dee\u304c\u3064\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
\u508d\u5fc3\u306f\u4e94\u5fc3\u306e\u306a\u304b\u3067\u306f\u30de\u30a4\u30ca\u30fc\u306a\u70b9\u3067\u3059\u3002<\/p>\n\n\n\n
\u300c\u5185\u5fc3\u300d<\/span>\u3084\u300c\u5916\u5fc3\u300d<\/span>\u306f\u91cd\u8981\u306a\u70b9\u306a\u306e\u3067\u5fc5\u305a\u78ba\u8a8d\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n\u508d\u5fc3\u4ee5\u5916\u306e\u4e94\u5fc3\u306b\u3064\u3044\u3066\u306f\u3053\u3061\u3089\u306e\u8a18\u4e8b\u3067\u307e\u3068\u3081\u307e\u3057\u305f<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"\u4e09\u89d2\u5f62\u306b\u306f\u4e94\u5fc3\u3068\u547c\u3070\u308c\u308b5\u3064\u306e\u70b9\u304c\u5b58\u5728\u3057\u307e\u3059\u3002 \u4eca\u56de\u306f\u4e94\u5fc3\u306e\u4e2d\u3067\u3082“\u508d\u5fc3”\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002 \u4e09\u89d2\u5f62\u306e\u508d\u5fc3\u3068\u306f\u30011\u3064\u306e\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u3068\u4ed6\u306e2\u3064\u306e\u5916\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u306e\u4ea4\u70b9\u3092\u6307\u3057\u307e\u3059\u3002 \u4e0a\u56f3\u304b\u3089\u5206\u304b\u308b\u3088 […]<\/p>\n","protected":false},"author":1,"featured_media":4918,"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-1721","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
\u4e09\u89d2\u5f62\u306e\u508d\u5fc3\u3068\u306f\uff1f\u6027\u8cea\u30fb\u610f\u5473\u30fb\u8a3c\u660e\u3092\u89e3\u8aac\uff01\u5185\u63a5\u5186\u3068\u306e\u9055\u3044\u3082\u89e3\u8aac<\/title>\n\n\n\n\n\n\n\n\n\n\n\n\t\n\t\n\t\n\n\n\n\n\t\n\t\n\t\n