{"id":1289,"date":"2015-09-23T00:25:50","date_gmt":"2015-09-22T15:25:50","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1289"},"modified":"2021-09-16T09:48:15","modified_gmt":"2021-09-16T00:48:15","slug":"thr201505","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201505\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2015\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(t \\gt 0\\) \u3092\u5b9f\u6570\u3068\u3059\u308b. \u5ea7\u6a19\u5e73\u9762\u306b\u304a\u3044\u3066, \\(3\\) \u70b9 A \\(( -2 , 0 )\\) , B \\(( 2 , 0 )\\) , C \\(( t , \\sqrt{3} t )\\) \u3092\u9802\u70b9\u3068\u3059\u308b\u4e09\u89d2\u5f62 ABP \u3092\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u4e09\u89d2\u5f62 ABP \u304c\u92ed\u89d2\u4e09\u89d2\u5f62\u3068\u306a\u308b\u3088\u3046\u306a \\(t\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u4e09\u89d2\u5f62 ABP \u306e\u5782\u5fc3\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000\u8fba AB , BP , PA \u306e\u4e2d\u70b9\u3092\u305d\u308c\u305e\u308c M, Q, R \u3068\u304a\u304f. \\(t\\) \u304c <strong>(1)<\/strong> \u3067\u6c42\u3081\u305f\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d, \u4e09\u89d2\u5f62 ABP \u3092\u7dda\u5206 MQ , QR , RM \u3067\u6298\u308a\u66f2\u3052\u3066\u3067\u304d\u308b\u56db\u9762\u4f53\u306e\u4f53\u7a4d\u306e\u6700\u5927\u5024\u3068, \u305d\u306e\u3068\u304d\u306e \\(t\\) \u306e\u5024\u3092\u6c42\u3081\u3088. ,<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u6761\u4ef6\u3088\u308a, \\(\\angle \\text{A}\\) \u304c\u920d\u89d2\u306b\u306a\u308b\u3053\u3068\u306f\u306a\u3044.<\/p>\r\n<ul>\r\n<li><p>\\(\\angle \\text{B}\\) \u304c\u920d\u89d2\u306b\u306a\u308b\u3068\u304d<br \/>\r\n\u70b9 P \u304c\u76f4\u7dda \\(x = 2\\) \u3088\u308a\u53f3\u5074\u306b\u3042\u308b\u3068\u304d\u306a\u306e\u3067\r\n\\[\r\nt \\gt 2 \\ .\r\n\\]<\/li>\r\n<li><p>\\(\\angle \\text{P}\\) \u304c\u920d\u89d2\u306b\u306a\u308b\u3068\u304d<br \/>\r\n\u5186\u5468\u89d2\u306e\u5b9a\u7406\u304b\u3089, \u70b9 P \u304c AB \u3092\u76f4\u5f84\u3068\u3059\u308b\u5186\u306e\u5185\u90e8\u306b\u3042\u308b\u3068\u304d\u3067\r\n\\[\r\n0 \\lt t \\lt 1\r\n\\]<\/li>\r\n<\/ul>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u6761\u4ef6\u306f\r\n\\[\r\n\\underline{1 \\leqq t \\leqq 2} \\ .\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u5782\u5fc3\u3092 H \u3068\u304a\u304f\u3068, PH \u3068 \\(x\\) \u8ef8\u306f\u5782\u76f4\u306a\u306e\u3067, H \\(( t , s )\\) \u3068\u304a\u3051\u308b.\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{AP}} & = ( t+2 , \\sqrt{3} ) , \\\\\r\n\\overrightarrow{\\text{BH}} & = ( t-2 , s ) \\ .\r\n\\end{align}\\]\r\n\\(\\overrightarrow{\\text{AP}} \\perp \\overrightarrow{\\text{BH}}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{AP}} \\cdot \\overrightarrow{\\text{BH}} & = t^2 -4 +\\sqrt{3} ts = 0 \\\\\r\n\\text{\u2234} \\quad & s = \\dfrac{4 -t^2}{\\sqrt{3} t} \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\text{H} \\ \\underline{\\left( t , \\dfrac{4 -t^2}{\\sqrt{3} t} \\right)} \\ .\r\n\\]\r\n<p><strong>(3)<\/strong><\/p>\r\n<p>\u56db\u9762\u4f53\u306e M, Q, R \u4ee5\u5916\u306e\u9802\u70b9\u3092 T \u3068\u3059\u308b.<br \/>\r\n\u4e2d\u7dda\u9023\u7d50\u5b9a\u7406\u3088\u308a, \u6298\u308a\u76ee\u306f\u5404\u8fba\u3068\u5e73\u884c\u3067\u3042\u308b\u304b\u3089, QR \u3092\u6298\u308a\u66f2\u3052\u308b\u3068, \u70b9 P \u306f PH \u3092\u542b\u307f \\(xy\\) \u5e73\u9762\u306b\u5782\u76f4\u306a\u5e73\u9762\u4e0a\u3092\u52d5\u304f.<br \/>\r\n\u70b9 A, B \u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306b\u8003\u3048\u308c\u3070, \u70b9 T \u306f \u70b9 H \u3092\u901a\u308a \\(xy\\) \u5e73\u9762\u306b\u5782\u76f4\u306a\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u3068\u3044\u3048\u308b.<br \/>\r\n\\(\\text{TH} = h\\) \u3068\u304a\u3044\u3066, \\(\\triangle \\text{MHT}\\) \u306b\u7740\u76ee\u3059\u308c\u3070, \u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3088\u308a\r\n\\[\\begin{align}\r\nh^2 & = \\text{AM}^2 -\\text{MH}^2 \\\\\r\n& = 2^2 -t^2 -\\dfrac{( 4 -t^2 )^2}{3 t^2} \\\\\r\n& = \\dfrac{( 4 -t^2 ) ( 3t^2 -4 +t^2 )}{3 t^2} \\\\\r\n& = \\dfrac{4 ( 4 -t^2 ) ( t^2 -1 )}{3 t^2} \\ .\r\n\\end{align}\\]\r\n\u307e\u305f\r\n\\[\\begin{align}\r\n\\triangle \\text{MQR} & = \\dfrac{1}{4} \\triangle \\text{ABP} \\\\\r\n& = \\dfrac{1}{4}\\cdot \\dfrac{1}{2} \\cdot 4 \\cdot 3 \\sqrt{t} = \\dfrac{\\sqrt{3} t}{2} \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u56db\u9762\u4f53\u306e\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\\begin{align}\r\nV & = \\dfrac{1}{3} \\cdot \\dfrac{\\sqrt{3} t}{2} \\cdot \\dfrac{2 \\sqrt{( 4 -t^2 ) ( t^2 -1 )}}{\\sqrt{3} t} \\\\\r\n& = \\dfrac{1}{3} \\sqrt{-t^4 +5t^2 -4} \\\\\r\n& = \\dfrac{1}{3} \\sqrt{-\\left( t^2 -\\dfrac{5}{2} \\right)^2 +\\dfrac{9}{4}} \\\\\r\n& \\leqq \\dfrac{1}{3} \\cdot \\dfrac{3}{2} = \\dfrac{1}{2} \\ .\r\n\\end{align}\\]\r\n\u3059\u306a\u308f\u3061, \u6c42\u3081\u308b\u6700\u5927\u5024\u306f\r\n\\[\r\n\\underline{\\dfrac{1}{2}} \\ .\r\n\\]\r\n\u3053\u306e\u3068\u304d\u306e \\(t\\) \u306e\u5024\u306f\r\n\\[\r\nt = \\sqrt{\\dfrac{5}{2}} = \\underline{\\dfrac{\\sqrt{10}}{2}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(t \\gt 0\\) \u3092\u5b9f\u6570\u3068\u3059\u308b. \u5ea7\u6a19\u5e73\u9762\u306b\u304a\u3044\u3066, \\(3\\) \u70b9 A \\(( -2 , 0 )\\) , B \\(( 2 , 0 )\\) , C \\(( t , \\sqrt{3} t )\\) \u3092\u9802\u70b9\u3068\u3059\u308b\u4e09\u89d2\u5f62  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/thr201505\/\">\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":[131],"tags":[148,137],"class_list":["post-1289","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2015","tag-tohoku_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1289","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=1289"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1289\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1289"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1289"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}