{"id":636,"date":"2013-02-16T23:10:29","date_gmt":"2013-02-16T14:10:29","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=636"},"modified":"2021-09-10T21:32:35","modified_gmt":"2021-09-10T12:32:35","slug":"tok200703","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok200703\/","title":{"rendered":"\u6771\u5de5\u59272007\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\u4e00\u8fba\u306e\u9577\u3055\u304c \\(1\\) \u306e\u6b63\u516b\u89d2\u5f62 \\(A _ 1 A _ 2 \\cdots A _ 8\\) \u306e\u5468\u4e0a\u3092 \\(3\\) \u70b9 \\(P , Q , R\\) \u304c\u52d5\u304f\u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(\\triangle PQR\\) \u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(Q\\) \u304c\u6b63\u516b\u89d2\u5f62\u306e\u9802\u70b9 \\(A _ 1\\) \u306b\u4e00\u81f4\u3057, \\(\\angle PQR = 90^{\\circ}\\) \u3068\u306a\u308b\u3068\u304d \\(\\triangle PQR\\) \u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/toko_2007_03_01.png\" alt=\"toko_2007_03_01\" class=\"aligncenter size-full\" \/>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u307e\u305a\u70b9 \\(P\\) \u306e\u4f4d\u7f6e\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u3068, \u8fba \\(QR\\) \u306b\u5e73\u884c\u306a\u76f4\u7dda \\(\\ell\\) \u304c\u6b63\u516b\u89d2\u5f62\u3068\u5171\u6709\u70b9\u3092\u3082\u3064\u3088\u3046\u306b\u52d5\u304b\u3057\u3066, \u8fba \\(QR\\) \u304b\u3089\u6700\u3082\u96e2\u308c\u3066\u3044\u308b\u3068\u304d, \\(\\triangle PQR\\) \u306e\u9762\u7a4d\u306f\u6700\u5927\u306b\u306a\u308b.<br \/>\r\n\u3053\u308c\u306f, \u70b9 \\(P\\) \u304c\u3042\u308b\u9802\u70b9\u306b\u4e00\u81f4\u3057\u3066\u3044\u308b\u5834\u5408\u3067\u3042\u308b.<br \/>\r\n\u4ed6\u306e \\(2\\) \u70b9 \\(Q , R\\) \u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306e\u3053\u3068\u304c\u6210\u7acb\u3059\u308b\u306e\u3067, \\(\\triangle PQR\\) \u304c\u6700\u5927\u306b\u306a\u308b\u306e\u306f \\(3\\) \u70b9 \\(P , Q , R\\) \u304c\u3059\u3079\u3066\u3044\u305a\u308c\u304b\u306e\u9802\u70b9\u306b\u4e00\u81f4\u3059\u308b\u3068\u304d\u3067\u3042\u308b.<br \/>\r\n\u3057\u305f\u304c\u3063\u3066, \u6700\u5927\u5024\u3092\u3068\u308b\u5019\u88dc\u3068\u306a\u308b \\(\\triangle PQR\\) \u306f\u4e0b\u56f3\u306e [1] \uff5e [4] \u306e\u5834\u5408\u3067\u3042\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/toko_2007_03_02.png\" alt=\"toko_2007_03_02\" class=\"aligncenter size-full\" \/>\r\n<ol>\r\n<li>[1] \u306e\u3068\u304d\r\n\\[\r\nPR = 1 +2 \\cdot \\dfrac{\\sqrt{2}}{2} = 1 +\\sqrt{2}\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\triangle PQR & = \\dfrac{1}{2} \\cdot 1 \\left( 1 +\\sqrt{2} \\right) \\\\\r\n& = \\dfrac{1 +\\sqrt{2}}{2}\r\n\\end{align}\\]<\/li>\r\n<li>[2] \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nPR & = 1 +\\sqrt{2} \\\\\r\nQH & = 1 +\\dfrac{\\sqrt{2}}{2} = \\dfrac{2 +\\sqrt{2}}{2}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\triangle PQR & = \\dfrac{1}{2} \\left( 1 +\\sqrt{2} \\right) \\cdot \\dfrac{2 +\\sqrt{2}}{2} \\\\\r\n& = \\dfrac{4 +3 \\sqrt{2}}{4}\r\n\\end{align}\\]<\/li>\r\n<li>[3] \u306e\u3068\u304d\r\n[2] \u306e\u3068\u304d\u3068\u540c\u3058\u4e09\u89d2\u5f62\u306a\u306e\u3067,\r\n\\[\r\n\\triangle PQR = \\dfrac{4 +3 \\sqrt{2}}{4}\r\n\\]<\/li>\r\n<li>[4] \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nPR & = QR = \\sqrt{1^2 +1^2 -2 \\cdot 1 \\cdot 1 \\cdot \\sin 135^{\\circ}} \\\\\r\n& = \\sqrt{2 +\\sqrt{2}}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\triangle PQR & = \\dfrac{1}{2} \\left( \\sqrt{2 +\\sqrt{2}} \\right)^2 \\\\\r\n& = \\dfrac{2 +\\sqrt{2}}{2}\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u9762\u7a4d\u306e\u6700\u5927\u5024\u306f\r\n\\[\r\n\\underline{\\dfrac{4 +3 \\sqrt{2}}{4}}\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(QP , QR\\) \u306e\u5ef6\u9577\u7dda\u3068\u6b63\u516b\u89d2\u5f62\u306e\u5916\u63a5\u5186\u306e\u4ea4\u70b9\u3092\u305d\u308c\u305e\u308c \\(P' , R'\\) \u3068\u304a\u304f.<br \/>\r\n\\(\\angle PQR = 90^{\\circ}\\) \u3068\u306a\u308b\u306e\u306f, \\(P'R'\\) \u304c\u5916\u63a5\u5186\u306e\u76f4\u5f84\u3068\u306a\u308b\u3068\u304d\u3067\u3042\u308b.<br \/>\r\n\u307e\u305f\r\n\\[\r\n\\triangle PQR \\leqq \\triangle PQ'R' \\quad ... [5]\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(P=P' , \\ R=R'\\) \u306e\u3068\u304d\u3067\u3042\u308b.<br \/>\r\n\u3055\u3089\u306b\r\n\\[\r\n\\triangle PQ'R' \\leqq \\triangle A _ {1}A _ {3}A _ {7}\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(P=A _ {3} , \\ R=A _ {7}\\) \u306e\u3068\u304d\u3067, \u3053\u308c\u306f [5] \u306e\u7b49\u53f7\u6210\u7acb\u306e\u6761\u4ef6\u3082\u6e80\u305f\u3057\u3066\u3044\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/toko_2007_03_03.png\" alt=\"toko_2007_03_03\" class=\"aligncenter size-full\" \/>\r\n<p>\u3053\u308c\u306f, <strong>(1)<\/strong> \u306e [4] \u306e\u3068\u304d\u3068\u540c\u3058\u4e09\u89d2\u5f62\u306a\u306e\u3067, \u6c42\u3081\u308b\u9762\u7a4d\u306e\u6700\u5927\u5024\u306f\r\n\\[\r\n\\underline{\\dfrac{2 +\\sqrt{2}}{2}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4e00\u8fba\u306e\u9577\u3055\u304c \\(1\\) \u306e\u6b63\u516b\u89d2\u5f62 \\(A _ 1 A _ 2 \\cdots A _ 8\\) \u306e\u5468\u4e0a\u3092 \\(3\\) \u70b9 \\(P , Q , R\\) \u304c\u52d5\u304f\u3068\u3059\u308b. (1)\u3000\\(\\triangle PQR\\) \u306e\u9762\u7a4d\u306e\u6700 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tok200703\/\">\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":[91],"tags":[141,109],"class_list":["post-636","post","type-post","status-publish","format-standard","hentry","category-toko_2007","tag-toko","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/636","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=636"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/636\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=636"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=636"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}