{"id":174,"date":"2011-12-02T22:29:31","date_gmt":"2011-12-02T13:29:31","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=174"},"modified":"2021-03-24T08:15:04","modified_gmt":"2021-03-23T23:15:04","slug":"kyr200902","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr200902\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb\u4e592009\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5e73\u9762\u4e0a\u306e\u92ed\u89d2\u4e09\u89d2\u5f62 \u25b3ABC \u306e\u5185\u90e8\uff08\u8fba\u3084\u9802\u70b9\u306f\u542b\u307e\u306a\u3044\uff09\u306b\u70b9 P \u3092\u3068\u308a, A' \u3092 B, C, P \u3092\u901a\u308b\u5186\u306e\u4e2d\u5fc3,\r\nB' \u3092 C, A, P \u3092\u901a\u308b\u5186\u306e\u4e2d\u5fc3, C' \u3092 A, B, P \u3092\u901a\u308b\u5186\u306e\u4e2d\u5fc3\u3068\u3059\u308b.\r\n\u3053\u306e\u3068\u304d A, B, C, A', B', C' \u304c\u540c\u4e00\u5186\u5468\u4e0a\u306b\u3042\u308b\u305f\u3081\u306e\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u306f P \u304c \u25b3ABC \u306e\u5185\u5fc3\u306b\u4e00\u81f4\u3059\u308b\u3053\u3068\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<ol>\r\n<li>[P] : \u300c A, B, C, A', B', C' \u304c\u540c\u4e00\u5186\u5468\u4e0a\u306b\u3042\u308b. \u300d<\/p><\/li>\r\n<li>[Q] : \u300c P \u304c \u25b3ABC \u306e\u5185\u5fc3\u3067\u3042\u308b. \u300d<\/p><\/li>\r\n<\/ol>\r\n<p>\\(\\angle \\text{A} =2a\\) , \\(\\angle \\text{B} =2b\\) , \\(\\angle \\text{C} =2c\\) \u3068\u304a\u304f\u3068\r\n\\[\r\na+b+c = \\dfrac{\\pi}{2} \\quad ... [1]\r\n\\]\r\n<ul>\r\n<li><p>\\([ \\text{Q} ] \\Rightarrow [ \\text{P} ]\\) \u306e\u8a3c\u660e<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyoto_r1_200902_01.png\" alt=\"\" title=\"kyoto_r1_200902_01\" class=\"aligncenter size-full\" \/>\r\n<p>P \u306f \u25b3ABC \u306e\u5185\u5fc3\u306a\u306e\u3067\r\n\\[\r\n\\angle \\text{PAB} = a , \\ \\angle \\text{PBC} = b , \\ \\angle \\text{PCB} = c\r\n\\]\r\nA, B, P \u306f C' \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u5186\u5468\u4e0a\u306e\u70b9\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\angle \\text{BC'P} & = 2a \\quad ... [2] \\\\\r\n\\text{\u2234} \\quad \\angle \\text{C'PB} & =\\dfrac{\\pi -2a}{2} = \\dfrac{\\pi}{2} -a \\quad ... [3]\r\n\\end{align}\\]\r\nB, C, P \u306f A' \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u5186\u5468\u4e0a\u306e\u70b9\u306a\u306e\u3067, \u540c\u69d8\u306b\r\n\\[\\begin{align}\r\n\\angle \\text{PA'B} & = 2c , \\ \\angle \\text{PA'C} = 2b \\\\\r\n\\text{\u2234} \\quad \\angle \\text{BPA'} & = \\dfrac{\\pi}{2} -b , \\ \\angle \\text{CPA'} = \\dfrac{\\pi}{2} -c \\quad ... [4]\r\n\\end{align}\\]\r\n[3] [4] \u3092\u7528\u3044\u308c\u3070\r\n\\[\r\n\\angle \\text{CPC'} = \\dfrac{3\\pi}{2} - (a+b+c) = \\pi \\quad ( \\ \\text{\u2235} \\ [1]\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, P\u306f\u7dda\u5206CC'\u4e0a\u306b\u5b58\u5728\u3059\u308b.<br \/>\r\n\u3086\u3048\u306b, [2] \u3088\u308a, \\(\\angle \\text{BAC} = \\angle \\text{BC'C}\\) \u306a\u306e\u3067, A, B, C, C'\u306f\u540c\u4e00\u5186\u5468\u4e0a\u306b\u5b58\u5728\u3059\u308b.<br \/>\r\n\u540c\u69d8\u306b\u3059\u308c\u3070, B', A' \u3082, A, B, C \u3068\u540c\u4e00\u5186\u5468\u4e0a\u306b\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u793a\u305b\u308b.<br \/>\r\n\u3088\u3063\u3066\r\n\\[\r\n[ \\text{Q} ] \\Rightarrow [ \\text{P} ]\r\n\\]<\/li>\r\n<li><p>\\([ \\text{P} ] \\Rightarrow [ \\text{Q} ]\\) \u306e\u8a3c\u660e<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyoto_r1_200902_02.png\" alt=\"\" title=\"kyoto_r1_200902_02\" class=\"aligncenter size-full\" \/>\r\n<p>\u6761\u4ef6\u3088\u308a, \\(\\text{A'B} =\\text{A'C}\\) , \\(\\text{B'C} =\\text{B'A}\\) , \\(\\text{C'A} =\\text{C'B}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\angle \\text{BAA'} = \\angle \\text{CAA'} & , \\ \\angle \\text{CBB'} = \\angle \\text{ABB'} , \\\\\r\n\\angle \\text{BCC'} & = \\angle \\text{ACC'} \\quad ... [5]\r\n\\end{align}\\]\r\n\u307e\u305f, \\(\\angle \\text{BC'A'} = \\angle \\text{CC'A'}\\) \u3059\u306a\u308f\u3061<br \/>\r\n\u300c A'C' \u306f \\(\\angle \\text{BC'C}\\) \u3092 \\(2\\) \u7b49\u5206\u3059\u308b. \u300d ... [6]\r\n\u6b21\u306b\u6761\u4ef6\u3088\u308a, \\(\\text{BC'} =\\text{PC'}\\) , \\(\\text{BA'} =\\text{PA'}\\) \u306a\u306e\u3067<br \/>\r\n\u300c A'C' \u306f \\(\\angle \\text{BC'P}\\) \u3092 \\(2\\) \u7b49\u5206\u3059\u308b. \u300d ... [7]\r\n\u3057\u305f\u304c\u3063\u3066, [6] [7] \u3088\u308a, P \u306f\u7dda\u5206 CC' \u4e0a\u306b\u5b58\u5728\u3059\u308b.<br \/>\r\n\u540c\u69d8\u306b\u3059\u308c\u3070<br \/>\r\n\u300c P\u306f\u7dda\u5206AA', BB'\u4e0a\u306b\u5b58\u5728\u3059\u308b. \u300d ... [8]\r\n[5] \u3088\u308a, AA', BB', CC' \u306f\u5404\u9802\u89d2 A, B, C \u306e \\(2\\) \u7b49\u5206\u7dda\u306a\u306e\u3067,\r\n\u5185\u5fc3\u306e\u4e00\u70b9\u3067\u4ea4\u308f\u308b\u304c, [8] \u3088\u308a, P \u304c\u5185\u5fc3\u306b\u4ed6\u306a\u3089\u306a\u3044.<br \/>\r\n\u3088\u3063\u3066\r\n\\[\r\n[ \\text{P} ] \\Rightarrow [ \\text{Q} ]\r\n\\]<\/li>\r\n<\/ul>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u5e73\u9762\u4e0a\u306e\u92ed\u89d2\u4e09\u89d2\u5f62 \u25b3ABC \u306e\u5185\u90e8\uff08\u8fba\u3084\u9802\u70b9\u306f\u542b\u307e\u306a\u3044\uff09\u306b\u70b9 P \u3092\u3068\u308a, A' \u3092 B, C, P \u3092\u901a\u308b\u5186\u306e\u4e2d\u5fc3, B' \u3092 C, A, P \u3092\u901a\u308b\u5186\u306e\u4e2d\u5fc3, C' \u3092 A, B, P \u3092\u901a\u308b\u5186\u306e\u4e2d\u5fc3\u3068\u3059\u308b. \u3053\u306e &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr200902\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[21],"tags":[140,15],"class_list":["post-174","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2009","tag-kyoto_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/174","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=174"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/174\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=174"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}