{"id":160,"date":"2011-12-01T18:14:47","date_gmt":"2011-12-01T09:14:47","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=160"},"modified":"2021-11-04T09:42:37","modified_gmt":"2021-11-04T00:42:37","slug":"htb201003","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201003\/","title":{"rendered":"\u4e00\u6a4b\u59272010\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u539f\u70b9\u3092 O \u3068\u3059\u308b \\(xyz\\) \u7a7a\u9593\u5185\u3067, \\(x\\) \u8ef8\u4e0a\u306e\u70b9 A , \\(xy\\) \u5e73\u9762\u4e0a\u306e\u70b9 B , \\(z\\) \u8ef8\u4e0a\u306e\u70b9 C \u3092, \u6b21\u3092\u307f\u305f\u3059\u3088\u3046\u306b\u5b9a\u3081\u308b.\r\n\\[\r\n\\angle \\text{OAC} = \\angle \\text{OBC} = \\theta , \\ \\angle \\text{AOB} = 2 \\theta , \\ \\text{OC} = 3\r\n\\]\r\n\u305f\u3060\u3057, A \u306e \\(x\\) \u5ea7\u6a19, B \u306e \\(y\\) \u5ea7\u6a19, C \u306e \\(z\\) \u5ea7\u6a19\u306f\u3044\u305a\u308c\u3082\u6b63\u3067\u3042\u308b.\r\n\u3055\u3089\u306b \u25b3ABC \u5185\u306e\u70b9\u306e\u3046\u3061, O \u304b\u3089\u306e\u8ddd\u96e2\u304c\u6700\u5c0f\u306e\u70b9\u3092 H \u3068\u3059\u308b. \u307e\u305f, \\(t = \\tan \\theta\\) \u3068\u304a\u304f.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u7dda\u5206 OH \u306e\u9577\u3055\u3092 \\(t\\) \u306e\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000H \u306e \\(z\\) \u5ea7\u6a19\u3092 \\(t\\) \u306e\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

    \u6761\u4ef6\u3088\u308a, \\(0^{\\circ} \\lt \\theta \\lt 90^{\\circ}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\cos \\theta & = \\dfrac{1}{\\sqrt{\\tan^2 \\theta +1}} = \\dfrac{1}{\\sqrt{t^2 +1}} , \\\\\r\n\\sin \\theta & = \\sqrt{1 -\\cos^2 \\theta} = \\dfrac{t}{\\sqrt{t^2 +1}}\r\n\\end{align}\\]\r\n\u307e\u305f\r\n\\[\r\n\\text{OA} = \\text{OB} = \\dfrac{3}{\\tan \\theta} = \\dfrac{3}{t}\r\n\\]\r\nAB \u306e\u4e2d\u70b9\u3092 M \u3068\u304a\u3051\u3070\r\n\\[\r\n\\text{OM} = \\text{OA} \\cos \\theta = \\dfrac{3}{t \\sqrt{t^2+1}}\r\n\\]\r\n\u3086\u3048\u306b\r\n\\[\\begin{align}\r\n\\text{CM} & = \\sqrt{\\text{OM}^2 +\\text{OC}^2} \\\\\r\n& = 3 \\sqrt{ \\dfrac{1}{t^2 \\left( t^2+1 \\right)} +1} \\\\\r\n& = \\dfrac{3\\sqrt{t^4+t^2 +1}}{t \\sqrt{t^2+1}}\r\n\\end{align}\\]\r\n\u56db\u9762\u4f53 OABC \u306f\u5e73\u9762 OMC \u306b\u3064\u3044\u3066\u5bfe\u79f0\u306a\u306e\u3067, \u70b9 H \u306f\u70b9 O \u304b\u3089 CM \u306b\u4e0b\u3057\u305f\u5782\u7dda\u306e\u8db3\u3067\u3042\u308b.
    \r\n\\(\\triangle \\text{OMC} \\sim \\triangle \\text{OHC}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\text{OH} : \\text{OC} & = \\text{OM} : \\text{CM} = 1 : \\sqrt{t^4+t^2 +1} \\\\\r\n\\text{\u2234} \\quad \\text{OH} & = \\underline{\\dfrac{3}{\\sqrt{t^4+t^2 +1}}}\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n

    \u70b9 H \u306f CH \u3092\r\n\\[\r\n\\text{OM}^2 : \\text{OC}^2 = t^2 \\left( t^2 +1 \\right) : 1\r\n\\]\r\n\u306b\u5185\u5206\u3059\u308b\u306e\u3067, \u70b9 H \u306e \\(z\\) \u5ea7\u6a19\u306f\r\n\\[\r\n\\dfrac{0 \\cdot t^2 \\left( t^2 +1 \\right) +3 \\cdot 1}{t^4 +t^2 +1} = \\underline{\\dfrac{3}{t^4 +t^2 +1}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u539f\u70b9\u3092 O \u3068\u3059\u308b \\(xyz\\) \u7a7a\u9593\u5185\u3067, \\(x\\) \u8ef8\u4e0a\u306e\u70b9 A , \\(xy\\) \u5e73\u9762\u4e0a\u306e\u70b9 B , \\(z\\) \u8ef8\u4e0a\u306e\u70b9 C \u3092, \u6b21\u3092\u307f\u305f\u3059\u3088\u3046\u306b\u5b9a\u3081\u308b. \\[ \\angle \\text{OAC} = \\a … \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":[46],"tags":[146,14],"class_list":["post-160","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2010","tag-hitotsubashi","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/160","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=160"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/160\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}