{"id":1342,"date":"2015-12-29T00:50:26","date_gmt":"2015-12-28T15:50:26","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1342"},"modified":"2021-10-30T20:02:03","modified_gmt":"2021-10-30T11:02:03","slug":"tkb201503","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201503\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2015\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\\(\\ell\\) \u3092\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u539f\u70b9\u3092\u901a\u308a\u50be\u304d\u304c\u6b63\u306e\u76f4\u7dda\u3068\u3059\u308b.\r\n\u3055\u3089\u306b, \u4ee5\u4e0b\u306e \\(3\\) \u6761\u4ef6 (i) , (ii) , (iii) \u3067\u5b9a\u307e\u308b\u5186 \\(C _ 1 , C _ 2\\) \u3092\u8003\u3048\u308b.<\/p>\r\n

    \r\n

  1. (i)\u3000\u5186 \\(C _ 1 , C _ 2\\) \u306f \\(2\\) \u3064\u306e\u4e0d\u7b49\u5f0f \\(x \\geqq 0\\) , \\(y \\geqq 0\\) \u3067\u5b9a\u307e\u308b\u9818\u57df\u306b\u542b\u307e\u308c\u308b.<\/p><\/li>\r\n

  2. (ii)\u3000\u5186 \\(C _ 1 , C _ 2\\) \u306f\u76f4\u7dda \\(\\ell\\) \u3068\u540c\u4e00\u70b9\u3067\u63a5\u3059\u308b.<\/p><\/li>\r\n

  3. (iii)\u3000\u5186 \\(C _ 1\\) \u306f \\(x\\) \u8ef8\u3068\u70b9 \\(( 1 , 0 )\\) \u3067\u63a5\u3057, \u5186 \\(C _ 2\\) \u306f \\(y\\) \u8ef8\u3068\u63a5\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n

    \u5186 \\(C _ 1\\) \u306e\u534a\u5f84\u3092 \\(r _ 1\\) , \u5186 \\(C _ 2\\) \u306e\u534a\u5f84\u3092 \\(r _ 2\\) \u3068\u3059\u308b.\r\n\\(8 r _ 1 +9 r _ 2\\) \u304c\u6700\u5c0f\u3068\u306a\u308b\u3088\u3046\u306a\u76f4\u7dda \\(\\ell\\) \u306e\u65b9\u7a0b\u5f0f\u3068, \u305d\u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n\"tkb20150301\"\r\n

    \r\n\r\n

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

    \\(C _ 1 , C _ 2\\) \u306e\u4e2d\u5fc3\u3092\u305d\u308c\u305e\u308c A , B , \\(C _ 1\\) \u3068 \\(C _ 2\\) \u306e\u63a5\u70b9\u3092 H \u3068\u304a\u304f.
    \r\n\u3053\u3053\u3067, \\(\\angle \\text{AOH} = \\theta \\ ( 0 \\lt \\theta \\lt 45^{\\circ} )\\) \u3068\u304a\u3051\u3070\r\n\\[\r\n\\text{OH} = 1 , \\quad \\angle \\text{BOH} = 45^{\\circ} -\\theta\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nr _ 1 & = \\tan \\theta , \\\\\r\nr _ 2 & = \\tan ( 45^{\\circ} -\\theta ) \\\\\r\n& = \\dfrac{1 -\\tan \\theta}{1 +1 \\cdot \\tan \\theta} \\\\\r\n& = \\dfrac{2}{r _ 1 +1} -1\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, \\(r _ 1\\) \u306e\u3068\u308a\u3046\u308b\u5024\u306e\u7bc4\u56f2\u306f, \\(0 \\lt r _ 1 \\lt 1\\) .
    \r\n\u3057\u305f\u304c\u3063\u3066, \u76f8\u52a0\u76f8\u4e57\u5e73\u5747\u306e\u95a2\u4fc2\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n8 r _ 1 +9 r _ 2 & = 8 r _ 1 -9 +\\dfrac{18}{r _ 1 +1} \\\\\r\n& = 8 ( r _ 1 +1 ) +\\dfrac{18}{r _ 1 +1} -17 \\\\\r\n& \\geqq 2 \\sqrt{8 ( r _ 1 +1 ) \\cdot \\dfrac{18}{r _ 1 +1}} -17 \\\\\r\n& = 2 \\cdot 12 -17 = 7\r\n\\end{align}\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f\r\n\\[\\begin{align}\r\n8 ( r _ 1 +1 ) & = \\dfrac{18}{r _ 1 +1} \\\\\r\n( r _ 1 +1 )^2 & = \\dfrac{9}{4} \\\\\r\n\\text{\u2234} \\quad r _ 1 & = \\dfrac{1}{2}\r\n\\end{align}\\]\r\n\u306e\u3068\u304d\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f \\(\\underline{7}\\) \u3067\u3042\u308a, \u3053\u306e\u3068\u304d\u306e \\(\\ell\\) \u306e\u5f0f\u306f\r\n\\[\\begin{align}\r\ny & = x \\tan 2 \\theta \\\\\r\n& = \\dfrac{2 \\cdot \\dfrac{1}{2}}{1 -\\left( \\dfrac{1}{2} \\right)^2} x \\\\\r\n& = \\dfrac{4}{3} x\r\n\\end{align}\\]\r\n\u3059\u306a\u308f\u3061\r\n\\[\r\n\\underline{y = \\dfrac{4}{3} x}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(\\ell\\) \u3092\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u539f\u70b9\u3092\u901a\u308a\u50be\u304d\u304c\u6b63\u306e\u76f4\u7dda\u3068\u3059\u308b. \u3055\u3089\u306b, \u4ee5\u4e0b\u306e \\(3\\) \u6761\u4ef6 (i) , (ii) , (iii) \u3067\u5b9a\u307e\u308b\u5186 \\(C _ 1 , C _ 2\\) \u3092\u8003\u3048\u308b. (i)\u3000\u5186 \\(C … \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":[135],"tags":[149,137],"class_list":["post-1342","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2015","tag-tokyo_b","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1342","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=1342"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1342\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1342"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1342"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}