{"id":1400,"date":"2017-03-10T21:09:45","date_gmt":"2017-03-10T12:09:45","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1400"},"modified":"2021-09-23T22:41:48","modified_gmt":"2021-09-23T13:41:48","slug":"tok201602","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok201602\/","title":{"rendered":"\u6771\u5de5\u59272016\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\\(\\triangle \\text{ABC}\\) \u3092\u4e00\u8fba\u306e\u9577\u3055 \\(6\\) \u306e\u6b63\u4e09\u89d2\u5f62\u3068\u3059\u308b. \u30b5\u30a4\u30b3\u30ed\u3092 \\(3\\) \u56de\u632f\u308a, \u51fa\u305f\u76ee\u3092\u9806\u306b \\(X , Y , Z\\) \u3068\u3059\u308b. \u51fa\u305f\u76ee\u306b\u5fdc\u3058\u3066, \u70b9 P, Q, R \u3092\u305d\u308c\u305e\u308c\u7dda\u5206 BC, CA, AB \u4e0a\u306b\r\n\\[\r\n\\overrightarrow{\\text{BP}} = \\dfrac{X}{6} \\overrightarrow{\\text{BC}} , \\quad \\overrightarrow{\\text{CQ}} = \\dfrac{Y}{6} \\overrightarrow{\\text{CA}} , \\quad \\overrightarrow{\\text{AR}} = \\dfrac{Z}{6} \\overrightarrow{\\text{AB}}\r\n\\]\r\n\u3092\u307f\u305f\u3059\u3088\u3046\u306b\u53d6\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\triangle \\text{PQR}\\) \u304c\u6b63\u4e09\u89d2\u5f62\u306b\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u70b9 B, P, R \u3092\u4e92\u3044\u306b\u7dda\u5206\u3067\u7d50\u3093\u3067\u3067\u304d\u308b\u56f3\u5f62\u3092 \\(T _ 1\\) , \u70b9 C, Q, P \u3092\u4e92\u3044\u306b\u7dda\u5206\u3067\u7d50\u3093\u3067\u3067\u304d\u308b\u56f3\u5f62\u3092 \\(T _ 2\\) , \u70b9 A, R, Q \u3092\u4e92\u3044\u306b\u7dda\u5206\u3067\u7d50\u3093\u3067\u3067\u304d\u308b\u56f3\u5f62\u3092 \\(T _ 3\\) \u3068\u3059\u308b. \\(T _ 1 , T _ 2 , T _ 3\\) \u306e\u3046\u3061, \u3061\u3087\u3046\u3069 \\(2\\) \u3064\u304c\u6b63\u4e09\u89d2\u5f62\u306b\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(\\triangle \\text{PQR}\\) \u306e\u9762\u7a4d\u3092 \\(S\\) \u3068\u3057, \\(S\\) \u306e\u3068\u308a\u3046\u308b\u5024\u306e\u6700\u5c0f\u5024\u3092 \\(m\\) \u3068\u3059\u308b. \\(m\\) \u306e\u5024\u304a\u3088\u3073 \\(S = m\\) \u3068\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \\(\\text{PQ} = \\text{QR} = \\text{RP}\\) \u3068\u306a\u308b\u306e\u306f, \\(\\triangle \\text{CPQ} \\equiv \\triangle \\text{AQR} \\equiv \\triangle \\text{BRP}\\) \u306e\u3068\u304d, \u3059\u306a\u308f\u3061 \\(X = Y = Z\\) \u306e\u3068\u304d\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{6}{6^3} = \\underline{\\dfrac{1}{36}}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\(T _ 1\\) \u3068 \\(T _ 2\\) \u306e\u307f\u304c\u6b63\u4e09\u89d2\u5f62\u3068\u306a\u308b\u5834\u5408\u306f\r\n\\[\r\n( X , Y , Z ) = (1,5,5) , (2,4,4) , (4,2,2) , (5,1,1)\r\n\\]\r\n\u306e \\(4\\) \u901a\u308a.
    \r\n\\(T _ 2\\) \u3068 \\(T _ 3\\) , \\(T _ 3\\) \u3068 \\(T _ 1\\) \u306e\u5834\u5408\u3082\u540c\u69d8\u306b \\(4\\) \u901a\u308a\u305a\u3064\u3042\u308b\u306e\u3067, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{4 \\cdot 3}{6^3} = \\underline{\\dfrac{1}{18}}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n

    \\[\\begin{align}\r\nS & = \\triangle \\text{ABC} -\\triangle \\text{BPR} -\\triangle \\text{CQP} -\\triangle \\text{ARQ} \\\\\r\n& = \\dfrac{1}{2} \\cdot \\sin 60^{\\circ} \\left\\{ 6^2 -X(6-Z) -Y(6-X) -Z(6-Y) \\right\\} \\\\\r\n& = \\dfrac{\\sqrt{3}}{4} \\underline{\\left\\{ 36 -X(6-Z) -Y(6-X) -Z(6-Y) \\right\\}} _ {[1]}\r\n\\end{align}\\]\r\n[1] \u304c\u6700\u5c0f\u3068\u306a\u308b\u5834\u5408\u306b\u3064\u3044\u3066\u8003\u3048\u308b.
    \r\n[1] \u306f \\(X , Y , Z\\) \u306e\u6b21\u6570\u306f\u9ad8\u3005 \\(1\\) \u6b21\u306a\u306e\u3067, \\(X , Y , Z\\) \u306e\u3046\u3061 \\(1\\) \u3064\u3060\u3051\u3092\u5909\u6570\u3068\u307f\u306a\u3057\u305f\u3068\u304d\u306b, \u6700\u5927, \u6700\u5c0f\u3068\u306a\u308b\u306e\u306f, \u5909\u57df\u306e\u7aef\u306b\u3042\u305f\u308b \\(1\\) \u307e\u305f\u306f \\(6\\) \u306e\u3068\u304d\u306b\u9650\u3089\u308c\u308b.
    \r\n\u3057\u305f\u304c\u3063\u3066, \\(X \\leqq Y \\leqq Z \\ ... [2]\\) \u306e\u3082\u3068\u3067\u8003\u3048\u308b\u3068, \u6700\u5c0f\u5024\u3092\u3068\u308a\u3046\u308b \\(X,Y,Z\\) \u306e\u7d44\u5408\u305b\u306f, \u4ee5\u4e0b\u306e \\(4\\) \u901a\u308a<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\((X,Y,Z) = (1,1,1)\\) \u306e\u3068\u304d\r\n\\[\r\n[1] = 36 -3 \\cdot 5 = 21\r\n\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\((X,Y,Z) = (1,1,6)\\) \u306e\u3068\u304d\r\n\\[\r\n[1] = 36 -5 -6 \\cdot 5 = 1\r\n\\]<\/li>\r\n

    3. 3*<\/strong>\u3000\\((X,Y,Z) = (1,6,6)\\) \u306e\u3068\u304d\r\n\\[\r\n[1] = 36 -6 \\cdot 5 = 6\r\n\\]<\/li>\r\n

    4. 4*<\/strong>\u3000\\((X,Y,Z) = (6,6,6)\\) \u306e\u3068\u304d\r\n\\[\r\n[1] = 36\r\n\\]<\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u6700\u5c0f\u3068\u306a\u308b\u306e\u306f, 2*<\/strong> \u306e\u5834\u5408\u3067, \u3053\u306e\u3068\u304d\r\n\\[\r\nm = \\dfrac{\\sqrt{3}}{4} \\cdot 1 = \\underline{\\dfrac{\\sqrt{3}}{4}}\r\n\\]\r\n\u6761\u4ef6 [2] \u3092\u5916\u3057\u3066\u8003\u3048\u308c\u3070, \\(S = m\\) \u3068\u306a\u308b\u306e\u306f\r\n\\[\r\n( X , Y , Z ) = (1,1,6) , (1,6,1) , (6,1,1)\r\n\\]\r\n\u306e\u3068\u304d\u306a\u306e\u3067, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{3}{6^3} = \\underline{\\dfrac{1}{72}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(\\triangle \\text{ABC}\\) \u3092\u4e00\u8fba\u306e\u9577\u3055 \\(6\\) \u306e\u6b63\u4e09\u89d2\u5f62\u3068\u3059\u308b. \u30b5\u30a4\u30b3\u30ed\u3092 \\(3\\) \u56de\u632f\u308a, \u51fa\u305f\u76ee\u3092\u9806\u306b \\(X , Y , Z\\) \u3068\u3059\u308b. \u51fa\u305f\u76ee\u306b\u5fdc\u3058\u3066, \u70b9 P, Q, R … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[153],"tags":[141,162],"class_list":["post-1400","post","type-post","status-publish","format-standard","hentry","category-toko_2016","tag-toko","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1400","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=1400"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1400\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1400"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1400"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}