{"id":782,"date":"2013-05-08T22:33:15","date_gmt":"2013-05-08T13:33:15","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=782"},"modified":"2021-03-23T17:13:06","modified_gmt":"2021-03-23T08:13:06","slug":"kyr201301","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201301\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2013\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5e73\u884c\u56db\u8fba\u5f62 ABCD \u306b\u304a\u3044\u3066, \u8fba AB \u3092 \\(1 : 1\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 E, \u8fba BC \u3092 \\(2 : 1\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 F,\r\n\u8fba CD \u3092 \\(3 : 1\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 G \u3068\u3059\u308b. \u7dda\u5206 CE \u3068\u7dda\u5206 FG \u306e\u4ea4\u70b9\u3092 P \u3068\u3057,\r\n\u7dda\u5206 AP \u3092\u5ef6\u9577\u3057\u305f\u76f4\u7dda\u3068\u8fba BC \u306e\u4ea4\u70b9\u3092 Q \u3068\u3059\u308b\u3068\u304d, \u6bd4 \\(\\text{AP} : \\text{PQ}\\) \u3092\u6c42\u3081\u3088.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p>\\(\\overrightarrow{\\text{AB}} = \\overrightarrow{b}\\) , \\(\\overrightarrow{\\text{AD}} = \\overrightarrow{d}\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{AC}} & = \\overrightarrow{b} +\\overrightarrow{d} , \\quad \\overrightarrow{\\text{AE}} = \\dfrac{1}{2} \\overrightarrow{b} , \\\\\r\n\\overrightarrow{\\text{AF}} & = \\overrightarrow{b} +\\dfrac{2}{3} \\overrightarrow{d} , \\quad \\overrightarrow{\\text{AG}} = \\dfrac{1}{4} \\overrightarrow{b} +\\overrightarrow{d}\r\n\\end{align}\\]\r\n\u70b9 P \u306f, \u7dda\u5206 CE \u3068\u7dda\u5206 FG \u306e\u4ea4\u70b9\u306a\u306e\u3067, \u5b9f\u6570 \\(s , t \\quad ( 0 \\lt s \\lt 1 , \\ 0 \\lt t \\lt 1 )\\) \u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{AP}} & = (1-s) \\overrightarrow{\\text{AC}} +s , \\\\\r\n\\overrightarrow{\\text{AE}} & = \\left( 1 -\\dfrac{s}{2} \\right) \\overrightarrow{b} +(1-s) \\overrightarrow{d} \\quad ... [1]\r\n\\end{align}\\]\r\n\u307e\u305f\u306f\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{AP}} & = (1-t) \\overrightarrow{\\text{AF}} +t , \\\\\r\n\\overrightarrow{\\text{AG}} & = \\left( 1 -\\dfrac{3t}{4} \\right) \\overrightarrow{b} +\\left( \\dfrac{2}{3} +\\dfrac{t}{3} \\right) \\overrightarrow{d} \\quad ... [2]\r\n\\end{align}\\]\r\n\u3068\u8868\u305b\u308b.<br \/>\r\n\\(\\overrightarrow{b}\\) \u3068 \\(\\overrightarrow{d}\\) \u306f\u4e00\u6b21\u72ec\u7acb\u306a\u306e\u3067, [1] \u3068 [2] \u3092\u6bd4\u8f03\u3057\u3066\r\n\\[\\begin{align}\r\n& \\left\\{\\begin{array}{l} 1 -\\dfrac{s}{2} = 1 -\\dfrac{3t}{4} \\\\ 1-s = \\dfrac{2}{3} +\\dfrac{t}{3} \\end{array}\\right. \\\\\r\n& \\text{\u2234} \\quad s = \\dfrac{3}{11} , \\quad t = \\dfrac{2}{11}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{AP}} & = \\left(1 -\\dfrac{1}{2} \\cdot \\dfrac{3}{11} \\right) \\overrightarrow{b} +\\left(1 -\\dfrac{3}{11} \\right) \\overrightarrow{d} \\\\\r\n& = \\dfrac{19}{22} \\overrightarrow{b} +\\dfrac{8}{11} \\overrightarrow{d}\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u7528\u3044\u308c\u3070, \u70b9 Q \u306f\u7dda\u5206 BC \u4e0a\u306b\u3042\u308a, \u304b\u3064\u7dda\u5206 AP \u306e\u5ef6\u9577\u7dda\u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\r\n\\overrightarrow{\\text{AQ}} = \\dfrac{22}{19} \\overrightarrow{\\text{AP}}\r\n= \\overrightarrow{b} +\\dfrac{16}{19} \\overrightarrow{d}\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\text{AP} : \\text{PQ} = \\underline{19 : 3}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5e73\u884c\u56db\u8fba\u5f62 ABCD \u306b\u304a\u3044\u3066, \u8fba AB \u3092 \\(1 : 1\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 E, \u8fba BC \u3092 \\(2 : 1\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 F, \u8fba CD \u3092 \\(3 : 1\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 G \u3068\u3059\u308b. \u7dda\u5206 CE &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201301\/\">\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":[88],"tags":[140,111],"class_list":["post-782","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2013","tag-kyoto_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/782","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=782"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/782\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=782"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}