{"id":373,"date":"2025-03-28T00:09:16","date_gmt":"2025-03-27T16:09:16","guid":{"rendered":"https:\/\/tilearn.space\/?p=373"},"modified":"2025-03-28T00:09:16","modified_gmt":"2025-03-27T16:09:16","slug":"2024%e5%b1%8a%e5%ae%9d%e5%b1%b1%e5%8c%ba%e5%88%9d%e4%b8%89%e4%ba%8c%e6%a8%a1%e6%95%b0%e5%ad%a6%e8%af%95%e5%8d%b7%e7%b2%be%e8%ae%b2%ef%bc%88%e7%ac%ac25%e9%a2%98%ef%bc%89","status":"publish","type":"post","link":"https:\/\/tilearn.space\/?p=373","title":{"rendered":"2024\u5c4a\u5b9d\u5c71\u533a\u521d\u4e09\u4e8c\u6a21\u6570\u5b66\u8bd5\u5377\u7cbe\u8bb2\uff08\u7b2c25\u9898\uff09"},"content":{"rendered":"
\n

\u9898\u76ee\uff1a<\/strong><\/p>\n

25. \u5df2\u77e5 \\(AB\\) \u662f\u534a\u5706 \\(O\\) \u7684\u76f4\u5f84\uff0c\\(C\\) \u662f\u534a\u5706 \\(O\\) \u4e0a\u4e0d\u4e0e \\(A\\)\u3001\\(B\\) \u91cd\u5408\u7684\u70b9\uff0c\u5c06\u5f27 \\(AC\\) \u6cbf\u76f4\u7ebf \\(AC\\) \u7ffb\u6298\uff0c\u7ffb\u6298\u6240\u5f97\u7684\u5f27\u4ea4\u76f4\u5f84 \\(AB\\) \u4e8e\u70b9 \\(D\\)\uff0c\\(E\\) \u662f\u70b9 \\(D\\) \u5173\u4e8e\u76f4\u7ebf \\(AC\\) \u7684\u5bf9\u79f0\u70b9\u3002<\/p>\n

\"7769a5f4df72c21aee5f6c20390bb3ed\"<\/p>\n

(1) \u5982\u56fe\uff0c\u70b9 \\(D\\) \u6070\u597d\u843d\u5728\u70b9 \\(O\\) \u5904\u3002<\/p>\n<\/div>\n

\n

\u7528\u5c3a\u89c4\u4f5c\u56fe\u5728\u56fe\u4e2d\u4f5c\u51fa\u70b9 \\(E\\)\uff08\u4fdd\u7559\u4f5c\u56fe\u75d5\u8ff9\uff09\uff0c\u8fde\u63a5 \\(AE\\)\u3001\\(CE\\)\u3001\\(CD\\)\uff0c\u6c42\u8bc1\uff1a\u56db\u8fb9\u5f62 \\(ADCE\\) \u662f\u83f1\u5f62\uff1b<\/p>\n

\u8fde\u63a5 \\(BE\\)\uff0c\u4e0e \\(AC\\)\u3001\\(CD\\) \u5206\u522b\u4ea4\u4e8e\u70b9 \\(F\\)\u3001\\(G\\)\uff0c\u6c42 \\(\\frac{FG}{BE}\\) \u7684\u503c\uff1b<\/p>\n

(2) \u5982\u679c \\(AB=10, OD=1\\)\uff0c\u6c42\u6298\u75d5 \\(AC\\) \u7684\u957f\u3002<\/p>\n

\u8be6\u7ec6\u89e3\u7b54\uff1a<\/strong><\/p>\n

\"\"<\/p>\n

(1) \u8bc1\u660e\uff1a\\(E\\) \u662f\u70b9 \\(D\\) \u5173\u4e8e\u76f4\u7ebf \\(AC\\) \u7684\u5bf9\u79f0\u70b9\u3002<\/p>\n

\"04e0610f541ea4ac9325625626986456\"<\/p>\n

\\(AE = AD\\), \\(CE = CD\\)\u3002<\/p>\n

\\(AD = CD\\)\u3002<\/p>\n

\\(AE = AD = CE = CD\\)\u3002<\/p>\n

\u56db\u8fb9\u5f62 \\(ADCE\\) \u662f\u83f1\u5f62\u3002<\/p>\n

\\(CE \\parallel AD\\)\u3002<\/p>\n

\\(\\frac{CF}{AF} = \\frac{CE}{AB} = \\frac{1}{2}\\)\u3002<\/p>\n

\\(FG = \\frac{1}{3} EG\\), \\(EG = \\frac{1}{2} BE\\)\u3002<\/p>\n

\\(FG = \\frac{1}{6} BE\\), \\(\\frac{FG}{BE} = \\frac{1}{6}\\)\u3002<\/p>\n

(2) \u5f53\u70b9 \\(D\\) \u5728\u70b9 \\(O\\) \u53f3\u4fa7\u3002<\/p>\n

\u4f5c\u70b9 \\(D\\) \u5173\u4e8e\u76f4\u7ebf \\(AC\\) \u7684\u5bf9\u79f0\u70b9 \\(E\\)\uff0c\u8054\u7ed3 \\(DE\\)\u3001\\(AE\\)\u3002<\/p>\n

\"44f4ce76b12228483a3b6885c5906fad\"<\/p>\n

\u8fc7\u70b9 \\(O\\) \u4f5c \\(OG \\perp AE\\)\uff0c\u5782\u8db3\u4e3a\u70b9 \\(G\\)\u3002\u8fc7\u70b9 \\(C\\) \u4f5c \\(CH \\perp AB\\)\uff0c\u5782\u8db3\u4e3a\u70b9 \\(H\\)\u3002<\/p>\n

\\(\\angle AGO = \\angle OHC = 90^\\circ\\)\u3002<\/p>\n

\\(AE = AD\\), \\(DE \\perp AC\\), \\(\\angle 1 = \\angle 2\\)\u3002<\/p>\n

\\(AO = CO\\), \\(\\angle = \\angle 2\\)\u3002<\/p>\n

\\(\\angle COH = \\angle 2 + \\angle 3 = 2 \\angle 2\\)\u3002<\/p>\n

\\(\\angle OAG = \\angle 1 + \\angle 2 = 2 \\angle 2\\)\u3002<\/p>\n

\\(\\angle COH = \\angle OAG\\)\u3002<\/p>\n

\\(AO = CO\\), \\(\\triangle OAG \\cong \\triangle COH\\), \\(AG = OH\\)\u3002<\/p>\n

\\(AB = 10\\), \\(OD = 1\\), \\(AD = AE = 6\\)\u3002<\/p>\n

\"16cc86b765b220f25585ae0efb13d742\"<\/p>\n

\\(OG \\perp AE\\), \\(AG = \\frac{1}{2} AE = 3\\)\u3002<\/p>\n

\\(OH = 3\\), \\(AH = 8\\)\u3002<\/p>\n

\u5728 \\(Rt\\triangle COH\\) \u4e2d, \\(CH = \\sqrt{CO^2 – OH^2} = \\sqrt{5^2 – 3^2} = 4\\)\u3002<\/p>\n

\u5728 \\(Rt\\triangle ACH\\) \u4e2d, \\(AC = \\sqrt{AH^2 + CH^2} = \\sqrt{8^2 + 4^2} = 4\\sqrt{5}\\)\u3002<\/p>\n

\u5f53\u70b9 \\(D\\) \u5728\u70b9 \\(O\\) \u5de6\u4fa7\uff0c\u540c\u7406\u53ef\u5f97 \\(AC = \\sqrt{70}\\)\u3002<\/p>\n

\u7efc\u4e0a\u6240\u8ff0\uff1a\u6298\u75d5 \\(AC\\) \u7684\u957f\u4e3a \\(4\\sqrt{5}\\) \u6216\u8005 \\(\\sqrt{70}\\)\u3002<\/p>\n

\u76f8\u5173\u77e5\u8bc6\u70b9\u590d\u4e60\uff1a<\/strong><\/p>\n

1. \u83f1\u5f62\u7684\u6027\u8d28\uff1a\u5bf9\u89d2\u7ebf\u4e92\u76f8\u5782\u76f4\u5e73\u5206\uff0c\u56db\u8fb9\u76f8\u7b49\u3002<\/p>\n

2. \u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u52fe\u80a1\u5b9a\u7406\uff1a\u76f4\u89d2\u4e09\u89d2\u5f62\u4e24\u76f4\u89d2\u8fb9\u7684\u5e73\u65b9\u548c\u7b49\u4e8e\u659c\u8fb9\u7684\u5e73\u65b9\u3002<\/p>\n

3. \u5bf9\u79f0\u6027\uff1a\u70b9\u5173\u4e8e\u76f4\u7ebf\u7684\u5bf9\u79f0\u70b9\u5230\u76f4\u7ebf\u7684\u8ddd\u79bb\u76f8\u7b49\u3002<\/p>\n

\u6613\u9519\u63d0\u793a\u548c\u62d3\u5c55\uff1a<\/strong><\/p>\n

1. \u6ce8\u610f\u533a\u5206\u70b9 \\(D\\) \u5728\u70b9 \\(O\\) \u53f3\u4fa7\u548c\u5de6\u4fa7\u7684\u60c5\u51b5\uff0c\u4e0d\u540c\u7684\u4f4d\u7f6e\u4f1a\u5bfc\u81f4\u4e0d\u540c\u7684\u7ed3\u679c\u3002<\/p>\n

2. \u5728\u89e3\u9898\u8fc7\u7a0b\u4e2d\uff0c\u8981\u5145\u5206\u5229\u7528\u51e0\u4f55\u56fe\u5f62\u7684\u5bf9\u79f0\u6027\u548c\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u6027\u8d28\u3002<\/p>\n

3. \u89e3\u9898\u65f6\u8981\u6ce8\u610f\u7ec6\u8282\uff0c\u5982\u70b9 \\(D\\) \u7684\u4f4d\u7f6e\u53d8\u5316\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd\u3002<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u9898\u76ee\uff1a 25. \u5df2\u77e5 \\(AB\\) \u662f\u534a\u5706 \\(O\\) \u7684\u76f4\u5f84\uff0c\\(C\\) \u662f\u534a\u5706 \\(O\\) \u4e0a\u4e0d\u4e0e \\(A […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-373","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/373","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=373"}],"version-history":[{"count":1,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/373\/revisions"}],"predecessor-version":[{"id":379,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/373\/revisions\/379"}],"wp:attachment":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=373"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}