{"id":497,"date":"2012-11-30T21:30:23","date_gmt":"2012-11-30T12:30:23","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=497"},"modified":"2021-09-27T21:06:47","modified_gmt":"2021-09-27T12:06:47","slug":"thr201004","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201004\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2010\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u56db\u9762\u4f53 ABCD \u306b\u304a\u3044\u3066, \u8fba AB \u306e\u4e2d\u70b9\u3092 M , \u8fba CD \u306e\u4e2d\u70b9\u3092 N \u3068\u3059\u308b.\r\n\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u7b49\u5f0f\r\n\\[\r\n\\overrightarrow{\\text{PA}} +\\overrightarrow{\\text{PB}} = \\overrightarrow{\\text{PC}} +\\overrightarrow{\\text{PD}}\r\n\\]\r\n\u3092\u6e80\u305f\u3059\u70b9 P \u306f\u5b58\u5728\u3059\u308b\u304b. \u8a3c\u660e\u3092\u3064\u3051\u3066\u7b54\u3048\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u70b9 Q \u304c\u7b49\u5f0f\r\n\\[\r\n\\left| \\overrightarrow{\\text{QA}} +\\overrightarrow{\\text{QB}} \\right| = \\left| \\overrightarrow{\\text{QC}} +\\overrightarrow{\\text{QD}} \\right|\r\n\\]\r\n\u3092\u6e80\u305f\u3057\u306a\u304c\u3089\u52d5\u304f\u3068\u304d, \u70b9 Q \u304c\u63cf\u304f\u56f3\u5f62\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u70b9 R \u304c\u7b49\u5f0f\r\n\\[\r\n\\left| \\overrightarrow{\\text{RA}} \\right|^2 + \\left| \\overrightarrow{\\text{RB}} \\right|^2 = \\left| \\overrightarrow{\\text{RC}} \\right|^2 + \\left| \\overrightarrow{\\text{RD}} \\right|^2\r\n\\]\r\n\u3092\u6e80\u305f\u3057\u306a\u304c\u3089\u52d5\u304f\u3068\u304d, \u5185\u7a4d \\(\\overrightarrow{\\text{MN}} \\cdot \\overrightarrow{\\text{MR}}\\) \u306f R \u306e\u3068\u308a\u65b9\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  4. (4)<\/strong>\u3000(2)<\/strong> \u306e\u70b9 Q \u304c\u63cf\u304f\u56f3\u5f62\u3068 (3)<\/strong> \u306e\u70b9 R \u304c\u63cf\u304f\u56f3\u5f62\u304c\u4e00\u81f4\u3059\u308b\u305f\u3081\u306e\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u306f \\(\\left| \\overrightarrow{\\text{AB}} \\right| = \\left| \\overrightarrow{\\text{CD}} \\right|\\) \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

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

    \u4e0e\u3048\u3089\u308c\u305f\u7b49\u5f0f\u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{1}{2} \\left( \\overrightarrow{\\text{PA}} +\\overrightarrow{\\text{PB}} \\right) & = \\dfrac{1}{2} \\left( \\overrightarrow{\\text{PC}} +\\overrightarrow{\\text{PD}} \\right) \\\\\r\n\\text{\u2234} \\quad \\overrightarrow{\\text{PM}} & = \\overrightarrow{\\text{PN}}\r\n\\end{align}\\]\r\n\u56db\u9762\u4f53 ABCD \u306b\u304a\u3044\u3066, M \u3068 N \u304c\u4e00\u81f4\u3059\u308b\u3053\u3068\u306f\u306a\u3044\u306e\u3067, \u3053\u306e\u3088\u3046\u306a\u70b9 P \u306f\u5b58\u5728\u3057\u306a\u3044.<\/p>\r\n

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

    \u4e0e\u3048\u3089\u308c\u305f\u7b49\u5f0f\u3088\u308a\r\n\\[\\begin{align}\r\n\\left| \\dfrac{1}{2} \\left( \\overrightarrow{\\text{PA}} +\\overrightarrow{\\text{PB}} \\right) \\right| & = \\left| \\dfrac{1}{2} \\left( \\overrightarrow{\\text{PC}} +\\overrightarrow{\\text{PD}} \\right) \\right| \\\\\r\n\\text{\u2234} \\quad \\left| \\overrightarrow{\\text{QM}} \\right| & = \\left| \\overrightarrow{\\text{QN}} \\right|\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u70b9 Q \u306e\u63cf\u304f\u56f3\u5f62\u306f\r\n\\[\r\n\\underline{\\text{M\u3068N\u306e\u5782\u76f4\u4e8c\u7b49\u5206\u9762}}\r\n\\]\r\n

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

    \u4e0e\u3048\u3089\u308c\u305f\u7b49\u5f0f\u3088\u308a\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{\\text{RM}} +\\overrightarrow{\\text{MA}} \\right|^2 + \\left| \\overrightarrow{\\text{RM}} -\\overrightarrow{\\text{MA}} \\right|^2 & = \\left| \\overrightarrow{\\text{RN}} +\\overrightarrow{\\text{NC}} \\right|^2 + \\left| \\overrightarrow{\\text{RN}} -\\overrightarrow{\\text{NC}} \\right|^2 \\\\\r\n\\left| \\overrightarrow{\\text{RM}} \\right|^2 + \\left| \\overrightarrow{\\text{MA}} \\right|^2 & = \\left| \\overrightarrow{\\text{RN}} \\right|^2 + \\left| \\overrightarrow{\\text{NC}} \\right|^2 \\\\\r\n\\left( \\overrightarrow{\\text{RM}} +\\overrightarrow{\\text{RN}} \\right) \\cdot \\left( \\overrightarrow{\\text{RM}} -\\overrightarrow{\\text{RN}} \\right) & = \\left| \\overrightarrow{\\text{NC}} \\right|^2 -\\left| \\overrightarrow{\\text{MA}} \\right|^2 \\quad ... [1] \\\\\r\n\\left( 2 \\overrightarrow{\\text{MR}} -\\overrightarrow{\\text{MN}} \\right) \\cdot \\overrightarrow{\\text{MN}} & = \\left| \\overrightarrow{\\text{NC}} \\right|^2 -\\left| \\overrightarrow{\\text{MA}} \\right|^2 \\\\\r\n\\text{\u2234} \\quad \\overrightarrow{\\text{MR}} \\cdot \\overrightarrow{\\text{MN}} & = \\dfrac{1}{2} \\left( \\left| \\overrightarrow{\\text{MN}} \\right|^2 +\\left| \\overrightarrow{\\text{NC}} \\right|^2 -\\left| \\overrightarrow{\\text{MA}} \\right|^2 \\right)\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \\(\\overrightarrow{\\text{MR}} \\cdot \\overrightarrow{\\text{MN}}\\) \u306f\u4e00\u5b9a\u3067\u3042\u308b.<\/p>\r\n

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

    \u70b9 Q \u3068\u70b9 R \u306e\u63cf\u304f\u56f3\u5f62\u304c\u4e00\u81f4\u3059\u308b\u306e\u306f\r\n\\[\r\n\\left| \\overrightarrow{\\text{RM}} \\right| = \\left| \\overrightarrow{\\text{RN}} \\right| \\quad ... [2]\r\n\\]\r\n\u304c\u6210\u7acb\u3059\u308b\u3068\u304d\u3067\u3042\u308b.
    \r\n[2] \u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{\\text{RM}} \\right|^2 & = \\left| \\overrightarrow{\\text{RN}} \\right|^2 \\\\\r\n\\left( \\overrightarrow{\\text{RM}} +\\overrightarrow{\\text{RN}} \\right) \\cdot \\left( \\overrightarrow{\\text{RM}} -\\overrightarrow{\\text{RN}} \\right) & = 0 \\\\\r\n\\left| \\overrightarrow{\\text{NC}} \\right|^2 -\\left| \\overrightarrow{\\text{MA}} \\right|^2 & = 0 \\quad ( \\ \\text{\u2235} \\ [1] \\ ) \\\\\r\n\\left| \\overrightarrow{\\text{MA}} \\right|^2 & = \\left| \\overrightarrow{\\text{NC}} \\right|^2 \\\\\r\n\\left| \\overrightarrow{\\text{AB}} \\right|^2 & = \\left| \\overrightarrow{\\text{CD}} \\right|^2 \\\\\r\n\\text{\u2234} \\quad \\left| \\overrightarrow{\\text{AB}} \\right| & = \\left| \\overrightarrow{\\text{CD}} \\right|\r\n\\end{align}\\]\r\n\u9006\u3082\u6210\u7acb\u3059\u308b\u306e\u3067, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u56db\u9762\u4f53 ABCD \u306b\u304a\u3044\u3066, \u8fba AB \u306e\u4e2d\u70b9\u3092 M , \u8fba CD \u306e\u4e2d\u70b9\u3092 N \u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u7b49\u5f0f \\[ \\overrightarrow{\\text{PA}} +\\overrightarrow … \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":[74],"tags":[148,14],"class_list":["post-497","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2010","tag-tohoku_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/497","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=497"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/497\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}