{"id":1973,"date":"2021-11-16T08:17:27","date_gmt":"2021-11-15T23:17:27","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1973"},"modified":"2021-11-16T08:17:27","modified_gmt":"2021-11-15T23:17:27","slug":"kyr202105","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr202105\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2021\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(xy\\) \u5e73\u9762\u306b\u304a\u3044\u3066, \\(2\\) \u70b9 B \\(( -\\sqrt{3} , -1 )\\) , C \\(( \\sqrt{3} , -1 )\\) \u306b\u5bfe\u3057, \u70b9 A \u306f\u6b21\u306e\u6761\u4ef6 (\uff0a) \u3092\u6e80\u305f\u3059\u3068\u3059\u308b.<\/p>\r\n

    \r\n
  1. (\uff0a)\u3000\\(\\angle \\text{BAC} = \\dfrac{\\pi}{3}\\) \u304b\u3064\u70b9 A \u306e \\(y\\) \u5ea7\u6a19\u306f\u6b63.<\/li>\r\n<\/ol>\r\n

    \u3000\u6b21\u306e\u5404\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

      \r\n

    1. (1)<\/strong>\u3000\\(\\triangle \\text{ABC}\\) \u306e\u5916\u5fc3\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

    2. (2)<\/strong>\u3000\u70b9 A \u304c\u6761\u4ef6 (\uff0a) \u3092\u6e80\u305f\u3057\u306a\u304c\u3089\u52d5\u304f\u3068\u304d, \\(\\triangle \\text{ABC}\\) \u306e\u5782\u5fc3\u306e\u8ecc\u8de1\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

      \r\n\r\n

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

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

      \u5916\u63a5\u5186\u306e\u534a\u5f84\u3092 \\(R\\) \u3068\u3059\u308c\u3070, \u6b63\u5f26\u5b9a\u7406\u3088\u308a\r\n\\[\\begin{gather}\r\n\\dfrac{\\text{BC}}{\\sin \\angle \\text{BAC}} = \\dfrac{2\\sqrt{3}}{\\dfrac{\\sqrt{3}}{2}} = 2R \\\\\r\n\\text{\u2234} \\quad R = 2\r\n\\end{gather}\\]\r\n\u5916\u5fc3\u306f, BC \u306e\u5782\u76f4\u4e8c\u7b49\u5206\u7dda\u3067\u3042\u308b \\(y\\) \u8ef8\u4e0a\u306b\u3042\u308a, B , C \u304b\u3089\u306e\u8ddd\u96e2\u304c \\(2\\) \u3067\u3042\u308b\u70b9\u306f, \\(( 0 , 0 )\\) , \\(( 0 , -2 )\\) .
      \r\n\u3057\u305f\u304c\u3063\u3066, \u5916\u63a5\u5186\u306e\u5019\u88dc\u306f, \\(x^2 +y^2 = 4\\) , \\(x^2 +(y+2)^2 = 4\\) \u306e \\(2\\) \u3064\u304c\u3042\u308b\u304c, A \u306e \\(y\\) \u5ea7\u6a19\u304c\u6b63\u3068\u306a\u308a\u3046\u308b\u306e\u306f, \u524d\u8005\u306e\u307f.
      \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u5ea7\u6a19\u306f\r\n\\[\r\n\\underline{( 0 , 0 )}\r\n\\]\r\n

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

      A \\(( p , q )\\) \u3068\u304a\u304f\u3068, A \u306e\u52d5\u304f\u7bc4\u56f2\u306f\r\n\\[\r\np^2 +q^2 = 4 \\quad ( q \\gt 0 ) \\quad ... [1]\r\n\\]\r\n\u5782\u5fc3 H \\(( X , Y )\\) \u3068\u304a\u304f\u3068, \\(\\text{AH} \\perp \\text{BC}\\) \u306a\u306e\u3067\r\n\\[\r\np = X \\quad ... [2]\r\n\\]\r\n\u307e\u305f, \\(\\text{BH} \\perp \\text{AC}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{BH}} \\cdot \\overrightarrow{\\text{CA}} = \\left( \\begin{array}{c} X +\\sqrt{3} \\\\ Y+1 \\end{array} \\right) \\cdot \\left( \\begin{array}{c} p -\\sqrt{3} \\\\ q+1 \\end{array} \\right) & = 0 \\\\\r\n\\left( p +\\sqrt{3} \\right) \\left( p -\\sqrt{3} \\right) +(Y+1) (q+1) & = 0 \\quad ( \\ \\text{\u2235} \\ [2] \\ ) \\\\\r\n-q^2 +1 +(Y+1) (q+1) & = 0 \\quad ( \\ \\text{\u2235} \\ [1] \\text{\u3088\u308a}\\ p^2 = 4 -q^2 \\ ) \\\\\r\n( q+1 ) ( 2 -q +Y ) & = 0\r\n\\end{align}\\]\r\n\\(q+1 \\neq 0\\) \u306a\u306e\u3067\r\n\\[\r\nq = Y+2 \\quad ... [3]\r\n\\]\r\n[1] \u306b [2] [3] \u3092\u4ee3\u5165\u3057\u3066\r\n\\[\r\nX^2 +(Y+2)^2 = 4 \\quad ( Y \\gt -2 )\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u8ecc\u8de1\u306f\r\n\\[\r\n\\underline{\\text{\u534a\u5186} \\ : \\ x^2 +(y+2)^2 = 4 \\quad ( y \\gt -2 )}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u306b\u304a\u3044\u3066, \\(2\\) \u70b9 B \\(( -\\sqrt{3} , -1 )\\) , C \\(( \\sqrt{3} , -1 )\\) \u306b\u5bfe\u3057, \u70b9 A \u306f\u6b21\u306e\u6761\u4ef6 (\uff0a) \u3092\u6e80\u305f\u3059\u3068\u3059\u308b. (\uff0a)\u3000\\(\\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":[171],"tags":[140,165],"class_list":["post-1973","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2021","tag-kyoto_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1973","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=1973"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1973\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}