求高中数学竞赛有关圆的定理及推论？ 求关于初三数学圆的所有定理及其推论，急～～～
\u6c42\u9ad8\u4e2d\u6570\u5b66\u8054\u8d5b\u4e8c\u8bd5\u7684\u5e38\u7528\u5f15\u7406\u7ec4\u5408\u6570\u8bba\u6bd4\u8f83\u6563\uff0c\u6ca1\u4ec0\u4e48\u597d\u603b\u7ed3\u7684\u554a\u3002\u3002\u81f3\u4e8e\u5e73\u51e0\u6709\u51e0\u4e2a\u6bd4\u8f83\u5e38\u89c1\u7684\uff0c\u6211\u5217\u8868\u7ed9\u4f60\uff0c\u5185\u5bb9\u592a\u591a\u4e86\u6211\u4e5f\u4e0d\u65b9\u4fbf\u8868\u8ff0
\u301001\u3011Newton\u5b9a\u7406
\u301002\u3011\u83ab\u96f7\uff08F. Morley\uff09\u5b9a\u7406
\u301003\u3011\u5bc6\u514b\uff08Miquel\uff09\u70b9
\u301004\u3011Fermat\uff08\u8d39\u5c14\u9a6c\uff09\u70b9
\u301005\u3011\u6b27\u62c9\uff08Euler\uff09\u7ebf
\u301006\u3011\u725b\u987f\uff08Newton\uff09\u7ebf
\u301007\u3011\u65af\u7279\u74e6\u5c14\u7279\uff08Stewart\uff09\u5b9a\u7406
\u301008\u3011\u6258\u52d2\u5bc6\uff08P'tolemy\uff09\u5b9a\u7406
\u301009\u3011\u897f\u59c6\u677e\uff08Simson\uff09\u5b9a\u7406
\u301010\u3011\u53cd\u6f14
\u301011\u3011\u5782\u5fc3\u7ec4\u5b9a\u7406
\u301012\u3011\u9762\u79ef\u539f\u7406
\u301013\u3011\u5357\u5317\u6781
\u301014\u3011\u8774\u8776\u5b9a\u7406
\u301015\u3011\u201c\u9e21\u722a\u201d\u5b9a\u7406
\u301016\u3011\u201c\u9e2d\u722a\u201d\u5b9a\u7406
\u301017\u3011\u585e\u74e6\uff08Ceva\uff09\u5b9a\u7406
\u301018\u3011\u4e5d\u70b9\u5706
\u301019\u3011\u65af\u5e93\u817e\uff08Schooten\uff09\u516c\u5f0f\uff08\u89d2\u5e73\u5206\u7ebf\u957f\u516c\u5f0f\uff09
\u301020\u3011\u5916\u89d2\u5e73\u5206\u7ebf\u957f\u516c\u5f0f
\u301021\u3011\u9006\u5e73\u884c\u7ebf\uff08antiparallels\uff09
\u301022\u3011\u5e73\u65b9\u5dee\u539f\u7406
\u301023\u3011\u5e73\u65b9\u548c\u539f\u7406
\u301024\u3011\u5f20\u89d2\u5f15\u7406
\u301025\u3011Euler\u6052\u7b49\u5f0f
\u301026\u3011\u8c03\u548c\u56db\u8fb9\u5f62
\u301027\u3011\u914d\u6781
\u301028\u3011\u8c03\u548c\u70b9\u5217
\u301029\u3011\u76f8\u4ea4\u5f26\u5b9a\u7406\u3001\u5207\u5272\u7ebf\u5b9a\u7406
\u301030\u3011\u5916\u5fc3\u548c\u5782\u5fc3
\u301031\u3011\u5706\u5e42\u548c\u6839\u8f74
\u301032\u3011\u5b8c\u5168\u56db\u8fb9\u5f62\uff08\u56db\u7ebf\u5f62\uff09
\u3016\u5706\u7684\u5b9a\u4e49\u3017
\u51e0\u4f55\u8bf4\uff1a\u5e73\u9762\u4e0a\u5230\u5b9a\u70b9\u7684\u8ddd\u79bb\u7b49\u4e8e\u5b9a\u957f\u7684\u6240\u6709\u70b9\u7ec4\u6210\u7684\u56fe\u5f62\u53eb\u505a\u5706\u3002\u5b9a\u70b9\u79f0\u4e3a\u5706\u5fc3\uff0c\u5b9a\u957f\u79f0\u4e3a\u534a\u5f84\u3002
\u8f68\u8ff9\u8bf4\uff1a\u5e73\u9762\u4e0a\u4e00\u52a8\u70b9\u4ee5\u4e00\u5b9a\u70b9\u4e3a\u4e2d\u5fc3\uff0c\u4e00\u5b9a\u957f\u4e3a\u8ddd\u79bb\u8fd0\u52a8\u4e00\u5468\u7684\u8f68\u8ff9\u79f0\u4e3a\u5706\u5468\uff0c\u7b80\u79f0\u5706\u3002
\u96c6\u5408\u8bf4\uff1a\u5230\u5b9a\u70b9\u7684\u8ddd\u79bb\u7b49\u4e8e\u5b9a\u957f\u7684\u70b9\u7684\u96c6\u5408\u53eb\u505a\u5706\u3002
\u3016\u5706\u7684\u76f8\u5173\u91cf\u3017
\u5706\u5468\u7387\uff1a\u5706\u5468\u957f\u5ea6\u4e0e\u5706\u7684\u76f4\u5f84\u957f\u5ea6\u7684\u6bd4\u53eb\u505a\u5706\u5468\u7387\uff0c\u503c\u662f3.14159265358979323846\u2026\uff0c\u901a\u5e38\u7528\u03c0\u8868\u793a\uff0c\u8ba1\u7b97\u4e2d\u5e38\u53d63.1416\u4e3a\u5b83\u7684\u8fd1\u4f3c\u503c\u3002
\u5706\u5f27\u548c\u5f26\uff1a\u5706\u4e0a\u4efb\u610f\u4e24\u70b9\u95f4\u7684\u90e8\u5206\u53eb\u505a\u5706\u5f27\uff0c\u7b80\u79f0\u5f27\u3002\u5927\u4e8e\u534a\u5706\u7684\u5f27\u79f0\u4e3a\u4f18\u5f27\uff0c\u5c0f\u4e8e\u534a\u5706\u7684\u5f27\u79f0\u4e3a\u52a3\u5f27\u3002\u8fde\u63a5\u5706\u4e0a\u4efb\u610f\u4e24\u70b9\u7684\u7ebf\u6bb5\u53eb\u505a\u5f26\u3002\u7ecf\u8fc7\u5706\u5fc3\u7684\u5f26\u53eb\u505a\u76f4\u5f84\u3002
\u5706\u5fc3\u89d2\u548c\u5706\u5468\u89d2\uff1a\u9876\u70b9\u5728\u5706\u5fc3\u4e0a\u7684\u89d2\u53eb\u505a\u5706\u5fc3\u89d2\u3002\u9876\u70b9\u5728\u5706\u5468\u4e0a\uff0c\u4e14\u5b83\u7684\u4e24\u8fb9\u5206\u522b\u4e0e\u5706\u6709\u53e6\u4e00\u4e2a\u4ea4\u70b9\u7684\u89d2\u53eb\u505a\u5706\u5468\u89d2\u3002
\u5185\u5fc3\u548c\u5916\u5fc3\uff1a\u8fc7\u4e09\u89d2\u5f62\u7684\u4e09\u4e2a\u9876\u70b9\u7684\u5706\u53eb\u505a\u4e09\u89d2\u5f62\u7684\u5916\u63a5\u5706\uff0c\u5176\u5706\u5fc3\u53eb\u505a\u4e09\u89d2\u5f62\u7684\u5916\u5fc3\u3002\u548c\u4e09\u89d2\u5f62\u4e09\u8fb9\u90fd\u76f8\u5207\u7684\u5706\u53eb\u505a\u8fd9\u4e2a\u4e09\u89d2\u5f62\u7684\u5185\u5207\u5706\uff0c\u5176\u5706\u5fc3\u79f0\u4e3a\u5185\u5fc3\u3002
\u6247\u5f62\uff1a\u5728\u5706\u4e0a\uff0c\u7531\u4e24\u6761\u534a\u5f84\u548c\u4e00\u6bb5\u5f27\u56f4\u6210\u7684\u56fe\u5f62\u53eb\u505a\u6247\u5f62\u3002\u5706\u9525\u4fa7\u9762\u5c55\u5f00\u56fe\u662f\u4e00\u4e2a\u6247\u5f62\u3002\u8fd9\u4e2a\u6247\u5f62\u7684\u534a\u5f84\u6210\u4e3a\u5706\u9525\u7684\u6bcd\u7ebf\u3002
\u3016\u5706\u548c\u5706\u7684\u76f8\u5173\u91cf\u5b57\u6bcd\u8868\u793a\u65b9\u6cd5\u3017
\u5706\u2014\u2299 \u534a\u5f84\u2014r \u5f27\u2014\u2312 \u76f4\u5f84\u2014d
\u6247\u5f62\u5f27\u957f\uff0f\u5706\u9525\u6bcd\u7ebf\u2014l \u5468\u957f\u2014C \u9762\u79ef\u2014S
\u3016\u5706\u548c\u5176\u4ed6\u56fe\u5f62\u7684\u4f4d\u7f6e\u5173\u7cfb\u3017
\u5706\u548c\u70b9\u7684\u4f4d\u7f6e\u5173\u7cfb\uff1a\u4ee5\u70b9P\u4e0e\u5706O\u7684\u4e3a\u4f8b\uff08\u8bbeP\u662f\u4e00\u70b9\uff0c\u5219PO\u662f\u70b9\u5230\u5706\u5fc3\u7684\u8ddd\u79bb\uff09\uff0cP\u5728\u2299O\u5916\uff0cPO\uff1er\uff1bP\u5728\u2299O\u4e0a\uff0cPO\uff1dr\uff1bP\u5728\u2299O\u5185\uff0cPO\uff1cr\u3002
\u76f4\u7ebf\u4e0e\u5706\u67093\u79cd\u4f4d\u7f6e\u5173\u7cfb\uff1a\u65e0\u516c\u5171\u70b9\u4e3a\u76f8\u79bb\uff1b\u6709\u4e24\u4e2a\u516c\u5171\u70b9\u4e3a\u76f8\u4ea4\uff1b\u5706\u4e0e\u76f4\u7ebf\u6709\u552f\u4e00\u516c\u5171\u70b9\u4e3a\u76f8\u5207\uff0c\u8fd9\u6761\u76f4\u7ebf\u53eb\u505a\u5706\u7684\u5207\u7ebf\uff0c\u8fd9\u4e2a\u552f\u4e00\u7684\u516c\u5171\u70b9\u53eb\u505a\u5207\u70b9\u3002\u4ee5\u76f4\u7ebfAB\u4e0e\u5706O\u4e3a\u4f8b\uff08\u8bbeOP\u22a5AB\u4e8eP\uff0c\u5219PO\u662fAB\u5230\u5706\u5fc3\u7684\u8ddd\u79bb\uff09\uff1aAB\u4e0e\u2299O\u76f8\u79bb\uff0cPO\uff1er\uff1bAB\u4e0e\u2299O\u76f8\u5207\uff0cPO\uff1dr\uff1bAB\u4e0e\u2299O\u76f8\u4ea4\uff0cPO\uff1cr\u3002
\u4e24\u5706\u4e4b\u95f4\u67095\u79cd\u4f4d\u7f6e\u5173\u7cfb\uff1a\u65e0\u516c\u5171\u70b9\u7684\uff0c\u4e00\u5706\u5728\u53e6\u4e00\u5706\u4e4b\u5916\u53eb\u5916\u79bb\uff0c\u5728\u4e4b\u5185\u53eb\u5185\u542b\uff1b\u6709\u552f\u4e00\u516c\u5171\u70b9\u7684\uff0c\u4e00\u5706\u5728\u53e6\u4e00\u5706\u4e4b\u5916\u53eb\u5916\u5207\uff0c\u5728\u4e4b\u5185\u53eb\u5185\u5207\uff1b\u6709\u4e24\u4e2a\u516c\u5171\u70b9\u7684\u53eb\u76f8\u4ea4\u3002\u4e24\u5706\u5706\u5fc3\u4e4b\u95f4\u7684\u8ddd\u79bb\u53eb\u505a\u5706\u5fc3\u8ddd\u3002\u4e24\u5706\u7684\u534a\u5f84\u5206\u522b\u4e3aR\u548cr\uff0c\u4e14R\u2265r\uff0c\u5706\u5fc3\u8ddd\u4e3aP\uff1a\u5916\u79bbP\uff1eR+r\uff1b\u5916\u5207P=R+r\uff1b\u76f8\u4ea4R-r\uff1cP\uff1cR+r\uff1b\u5185\u5207P=R-r\uff1b\u5185\u542bP\uff1cR-r\u3002
\u3010\u5706\u7684\u5e73\u9762\u51e0\u4f55\u6027\u8d28\u548c\u5b9a\u7406\u3011
\u3016\u6709\u5173\u5706\u7684\u57fa\u672c\u6027\u8d28\u4e0e\u5b9a\u7406\u3017
\u5706\u7684\u786e\u5b9a\uff1a\u4e0d\u5728\u540c\u4e00\u76f4\u7ebf\u4e0a\u7684\u4e09\u4e2a\u70b9\u786e\u5b9a\u4e00\u4e2a\u5706\u3002
\u5706\u7684\u5bf9\u79f0\u6027\u8d28\uff1a\u5706\u662f\u8f74\u5bf9\u79f0\u56fe\u5f62\uff0c\u5176\u5bf9\u79f0\u8f74\u662f\u4efb\u610f\u4e00\u6761\u8fc7\u5706\u5fc3\u7684\u76f4\u7ebf\u3002\u5706\u4e5f\u662f\u4e2d\u5fc3\u5bf9\u79f0\u56fe\u5f62\uff0c\u5176\u5bf9\u79f0\u4e2d\u5fc3\u662f\u5706\u5fc3\u3002
\u5782\u5f84\u5b9a\u7406\uff1a\u5782\u76f4\u4e8e\u5f26\u7684\u76f4\u5f84\u5e73\u5206\u8fd9\u6761\u5f26\uff0c\u5e76\u4e14\u5e73\u5206\u5f26\u6240\u5bf9\u7684\u5f27\u3002\u9006\u5b9a\u7406\uff1a\u5e73\u5206\u5f26\uff08\u4e0d\u662f\u76f4\u5f84\uff09\u7684\u76f4\u5f84\u5782\u76f4\u4e8e\u5f26\uff0c\u5e76\u4e14\u5e73\u5206\u5f26\u6240\u5bf9\u7684\u5f27\u3002
\u3016\u6709\u5173\u5706\u5468\u89d2\u548c\u5706\u5fc3\u89d2\u7684\u6027\u8d28\u548c\u5b9a\u7406\u3017
\u5728\u540c\u5706\u6216\u7b49\u5706\u4e2d\uff0c\u5982\u679c\u4e24\u4e2a\u5706\u5fc3\u89d2\uff0c\u4e24\u4e2a\u5706\u5468\u89d2\uff0c\u4e24\u6761\u5f27\uff0c\u4e24\u6761\u5f26\u4e2d\u6709\u4e00\u7ec4\u91cf\u76f8\u7b49\uff0c\u90a3\u4e48\u4ed6\u4eec\u6240\u5bf9\u5e94\u7684\u5176\u4f59\u5404\u7ec4\u91cf\u90fd\u5206\u522b\u76f8\u7b49\u3002
\u4e00\u6761\u5f27\u6240\u5bf9\u7684\u5706\u5468\u89d2\u7b49\u4e8e\u5b83\u6240\u5bf9\u7684\u5706\u5fc3\u89d2\u7684\u4e00\u534a\u3002
\u76f4\u5f84\u6240\u5bf9\u7684\u5706\u5468\u89d2\u662f\u76f4\u89d2\u300290\u5ea6\u7684\u5706\u5468\u89d2\u6240\u5bf9\u7684\u5f26\u662f\u76f4\u5f84\u3002
\u3016\u6709\u5173\u5916\u63a5\u5706\u548c\u5185\u5207\u5706\u7684\u6027\u8d28\u548c\u5b9a\u7406\u3017
\u4e00\u4e2a\u4e09\u89d2\u5f62\u6709\u552f\u4e00\u786e\u5b9a\u7684\u5916\u63a5\u5706\u548c\u5185\u5207\u5706\u3002\u5916\u63a5\u5706\u5706\u5fc3\u662f\u4e09\u89d2\u5f62\u5404\u8fb9\u5782\u76f4\u5e73\u5206\u7ebf\u7684\u4ea4\u70b9\uff0c\u5230\u4e09\u89d2\u5f62\u4e09\u4e2a\u9876\u70b9\u8ddd\u79bb\u76f8\u7b49\uff1b\u5185\u5207\u5706\u7684\u5706\u5fc3\u662f\u4e09\u89d2\u5f62\u5404\u5185\u89d2\u5e73\u5206\u7ebf\u7684\u4ea4\u70b9\uff0c\u5230\u4e09\u89d2\u5f62\u4e09\u8fb9\u8ddd\u79bb\u76f8\u7b49\u3002
\u3016\u6709\u5173\u5207\u7ebf\u7684\u6027\u8d28\u548c\u5b9a\u7406\u3017
\u5706\u7684\u5207\u7ebf\u5782\u76f4\u4e8e\u8fc7\u5207\u70b9\u7684\u76f4\u5f84\uff1b\u7ecf\u8fc7\u76f4\u5f84\u7684\u4e00\u7aef\uff0c\u5e76\u4e14\u5782\u76f4\u4e8e\u8fd9\u6761\u76f4\u5f84\u7684\u76f4\u7ebf\uff0c\u662f\u8fd9\u4e2a\u5706\u7684\u5207\u7ebf\u3002
\u5207\u7ebf\u5224\u5b9a\u5b9a\u7406\uff1a\u7ecf\u8fc7\u534a\u5f84\u5916\u7aef\u5e76\u4e14\u5782\u76f4\u4e8e\u8fd9\u6761\u534a\u5f84\u7684\u76f4\u7ebf\u662f\u5706\u7684\u5207\u7ebf\u3002
\u5207\u7ebf\u7684\u6027\u8d28\uff1a\uff081\uff09\u7ecf\u8fc7\u5706\u5fc3\u5782\u76f4\u4e8e\u8fd9\u6761\u534a\u5f84\u7684\u76f4\u7ebf\u662f\u5706\u7684\u5207\u7ebf\u3002\uff082\uff09\u7ecf\u8fc7\u5207\u70b9\u5782\u76f4\u4e8e\u5207\u7ebf\u7684\u76f4\u7ebf\u5fc5\u7ecf\u8fc7\u5706\u5fc3\u3002\uff083\uff09\u5706\u7684\u5207\u7ebf\u5782\u76f4\u4e8e\u7ecf\u8fc7\u5207\u70b9\u7684\u534a\u5f84\u3002
\u5207\u7ebf\u7684\u957f\u5b9a\u7406\uff1a\u4ece\u5706\u5916\u4e00\u70b9\u5230\u5706\u7684\u4e24\u6761\u5207\u7ebf\u7684\u957f\u76f8\u7b49\u3002
\u3016\u6709\u5173\u5706\u7684\u8ba1\u7b97\u516c\u5f0f\u3017
1.\u5706\u7684\u5468\u957fC=2\u03c0r=\u03c0d 2.\u5706\u7684\u9762\u79efS=\u03c0r�0�5 3.\u6247\u5f62\u5f27\u957fl=n\u03c0r/180
4.\u6247\u5f62\u9762\u79efS=n\u03c0r�0�5/360=rl/2 5.\u5706\u9525\u4fa7\u9762\u79efS=\u03c0rl
\u3010\u5706\u7684\u89e3\u6790\u51e0\u4f55\u6027\u8d28\u548c\u5b9a\u7406\u3011
\u3016\u5706\u7684\u89e3\u6790\u51e0\u4f55\u65b9\u7a0b\u3017
\u5706\u7684\u6807\u51c6\u65b9\u7a0b\uff1a\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0c\u4ee5\u70b9O\uff08a\uff0cb\uff09\u4e3a\u5706\u5fc3\uff0c\u4ee5r\u4e3a\u534a\u5f84\u7684\u5706\u7684\u6807\u51c6\u65b9\u7a0b\u662f\uff08x-a\uff09^2+\uff08y-b\uff09^2=r^2\u3002
\u5706\u7684\u4e00\u822c\u65b9\u7a0b\uff1a\u628a\u5706\u7684\u6807\u51c6\u65b9\u7a0b\u5c55\u5f00\uff0c\u79fb\u9879\uff0c\u5408\u5e76\u540c\u7c7b\u9879\u540e\uff0c\u53ef\u5f97\u5706\u7684\u4e00\u822c\u65b9\u7a0b\u662fx^2+y^2+Dx+Ey+F=0\u3002\u548c\u6807\u51c6\u65b9\u7a0b\u5bf9\u6bd4\uff0c\u5176\u5b9eD=-2a\uff0cE=-2b\uff0cF=a^2+b^2\u3002
\u5706\u7684\u79bb\u5fc3\u7387e=0\uff0c\u5728\u5706\u4e0a\u4efb\u610f\u4e00\u70b9\u7684\u66f2\u7387\u534a\u5f84\u90fd\u662fr\u3002
绛旓細棣栧厛鏄畝鍗曠殑锛屼篃鏄渶鍩烘湰鐨勪笁澶у畾鐞嗭細鎵樺嫆瀵嗗畾鐞 姊呭唴鍔虫柉瀹氱悊鍜濉炵摝瀹氱悊锛涘叾娆℃槸绋嶅井鍩烘湰鐨勶細铦磋澏瀹氱悊锛岃タ濮嗘澗瀹氱悊锛岀墰椤垮畾鐞嗙瓑绛夊啀娆℃槸闃呭嵎鑰佸笀閮芥湭蹇呯煡閬鐨勫畾鐞锛屽ぇ澶氫笉鍙互鐩存帴鐢細鏉ユ懇鎭╁畾鐞嗭紙Lemoine锛夛紙杩囦笁瑙掑舰鐨勪笁涓《鐐逛綔鍏跺鎺鍦嗙殑鍒囩嚎锛屼笌瀵硅竟寤堕暱绾跨殑涓変釜浜ょ偣鍏辩嚎锛夊崱璇哄畾鐞嗭紙Carnot锛夛紙鍦ㄢ柍...
绛旓細1. 鍦嗙殑瀹氫箟锛氬钩闈㈠唴鍒颁竴瀹氱偣鐨勮窛绂荤瓑浜庡畾闀跨殑鐐圭殑杞ㄨ抗鍙仛鍦嗐傚畾鐐瑰彨鍦嗙殑鍦嗗績锛屽畾闀垮彨鍋氬渾鐨勫崐寰勩2. 鍦嗙殑鏍囧噯鏂圭▼锛氬凡鐭ュ渾蹇冧负锛坅锛宐锛夛紝鍗婂緞涓簉锛屽垯鍦嗙殑鏂圭▼涓(x-a)2+(y-b)2=r2銆傝鏄庯細锛1锛変笂寮忕О涓哄渾鐨勬爣鍑嗘柟绋嬨傦紙2锛夊鏋滃渾蹇冨湪鍧愭爣鍘熺偣锛岃繖鏃禷锛0锛宐锛0锛屽渾鐨勬柟绋嬪氨鏄痻2+y2=...
绛旓細璁続BP鏄姍O鐨勪竴鏉″壊绾匡紝PT鏄姍O鐨勪竴鏉″垏绾匡紝鍒囩偣涓篢锛屽垯PT²=PA路PB 4銆佸壊绾瀹氱悊 浠庡渾澶栦竴鐐瑰紩鍦嗙殑涓ゆ潯鍓茬嚎锛岃繖涓鐐瑰埌姣忔潯鍓茬嚎涓庡渾浜ょ偣鐨勮窛绂荤殑绉浉绛夈備竴鏉＄洿绾夸笌涓鏉″姬绾挎湁涓や釜鍏叡鐐癸紝鎴戜滑灏辫杩欐潯鐩寸嚎鏄繖鏉℃洸绾跨殑鍓茬嚎銆5銆佸瀭寮﹀畾鐞 鍨傜洿浜庡鸡鐨勭洿寰勫钩鍒嗚繖鏉″鸡锛屽苟涓斿钩鍒嗚繖鏉″鸡鎵...
绛旓細36瀹氱悊 鐩镐氦涓鍦嗙殑杩炲績绾垮瀭鐩村钩鍒嗕袱鍦嗙殑鍏叡寮 37瀹氱悊 鎶婂渾鍒嗘垚n(n鈮3): 鈶翠緷娆¤繛缁撳悇鍒嗙偣鎵寰楃殑澶氳竟褰㈡槸杩欎釜鍦嗙殑鍐呮帴姝杈瑰舰 鈶电粡杩囧悇鍒嗙偣浣滃渾鐨勫垏绾,浠ョ浉閭诲垏绾跨殑浜ょ偣涓洪《鐐圭殑澶氳竟褰㈡槸杩欎釜鍦嗙殑澶栧垏姝杈瑰舰 38瀹氱悊 浠讳綍姝ｅ杈瑰舰閮芥湁涓涓鎺ュ渾鍜屼竴涓唴鍒囧渾,杩欎袱涓渾鏄悓蹇冨渾 39姝杈瑰舰鐨勬瘡涓唴瑙掗兘绛変簬...
绛旓細鐩稿噺锛屽緱 a = 1 锛屽洜姝 r^2 = 4 锛屾墍浠ュ渾鏂圭▼涓 (x-1)^2+(y-1)^2=4 銆傦紙2锛夎 P锛4m锛-2-3m锛夋槸鐩寸嚎涓婁换涓鐐癸紝鐢变簬 PA涓凪A 锛屽洜姝ょ敱鍕捐偂瀹氱悊寰 PA^2=PM^2-MA^2=(4m-1)^2+(-2-3m-1)^2-4 = 25m^2+10m+6 锛屾墍浠ュ洓杈瑰舰 PAMB 鐨勯潰绉负 SPAMB=2SPAM=PA*MA=2鈭(...
绛旓細鑱旂珛锛坸-3)^2+y^2=4涓巠锛漦x鍙緱(k^2+1)x^2-6x+5锛0.鏍规嵁闊﹁揪瀹氱悊鍙煡x1*x2锛5/(k^2+1).璁綪涓嶲鐨勫潗鏍囧垎鍒负(x1,y1)(x2,y2)鎵浠P涓嶰Q闀夸负x1鈭(k^2+1)涓巟2鈭(k^2+1)銆傛墍浠ュ畠浠殑绉负x1x2*(k^2+1)鐢卞墠闈㈤煢杈惧畾鐞嗗彲鐭ョ瓟妗堜负5 ...
绛旓細鍒囩嚎闀垮畾鐞+鍒囧壊绾垮畾鐞+鐩镐氦寮瀹氱悊鍙鎺ㄨ锛夛紝鈥1鎺3鈥濆畾鐞嗭紙鍚屽渾鎴栫瓑鍦嗕腑鐨勪袱鏉″姬锛屼袱鏉″鸡鍙婂鸡蹇冭窛寮ф墍瀵瑰渾蹇冭涓湁涓缁勭浉绛夛紝鍏朵綑閮界浉绛夛級鐩村緞鎵瀵瑰渾鍛ㄨ鏄洿瑙掞紝90掳鐨勫渾鍛ㄨ鎵瀵圭殑寮︽槸鐩村緞 寮﹀垏瑙掑畾鐞 鍦嗗唴鎺ュ洓杈瑰舰鐨勬ц川鍜屽垽鏂畾鐞 鏃堕棿鍏崇郴锛岀洰鍓嶅彧鎯宠捣杩欎簺 甯屾湜瀵逛綘鏈夊府鍔 甯屾湜閲囩撼 ...
绛旓細楂樹腑鏁板涓殑鍦嗙殑鐭ヨ瘑鐐逛富瑕佸寘鎷互涓嬪嚑涓柟闈細1. 鍦嗙殑瀹氫箟锛氬渾鏄钩闈笂鎵鏈変笌瀹氱偣锛堝渾蹇冿級璺濈鐩哥瓑鐨勭偣鐨勯泦鍚堛傝繖涓畾鐐瑰彨鍋氬渾蹇冿紝杩欎釜璺濈鍙仛鍗婂緞銆2. 鍦嗙殑鎬ц川锛鍦嗗叿鏈鏃嬭浆涓嶅彉鎬э紝鍗冲渾涓婁换鎰忎竴鐐瑰叧浜庡渾蹇冪殑瀵圭О鐐逛篃鍦ㄥ渾涓婏紱鍦嗕笂浠绘剰涓ょ偣鍙互纭畾涓涓洿寰勶紱鍦嗕笂浠绘剰涓夌偣鍙互纭畾涓涓笁瑙掑舰銆3. ...
绛旓細鐩哥瓑,鎵瀵圭殑寮︾殑寮﹀績璺濈浉绛 10鎺ㄨ 鍦ㄥ悓鍦嗘垨绛夊渾涓,濡傛灉涓や釜鍦嗗績瑙掋佷袱鏉″姬銆佷袱鏉″鸡鎴栦袱 寮︾殑寮﹀績璺濅腑鏈変竴缁勯噺鐩哥瓑閭ｄ箞瀹冧滑鎵瀵瑰簲鐨勫叾浣欏悇缁勯噺閮界浉绛 11瀹氱悊 鍦嗙殑鍐呮帴鍥涜竟褰㈢殑瀵硅浜掕ˉ,骞朵笖浠讳綍涓涓瑙掗兘绛変簬瀹 鐨勫唴瀵硅 12鈶犵洿绾縇鍜屸姍O鐩镐氦 d锛渞 鈶＄洿绾縇鍜屸姍O鐩稿垏 d=r 鈶㈢洿绾縇鍜屸姍O...
绛旓細涓銆佸懆闀垮叕寮 1銆鍦嗙殑鍛ㄩ暱 锛欳=2蟺r 锛坮锛氬崐寰勶級2銆佸崐鍦嗗懆闀匡細C=蟺r+2r 浜屻佸渾鐨勯潰绉 1銆侀潰绉細S=蟺r²2銆佸崐鍦嗛潰绉細S=蟺r²/2 涓夈佸姬闀胯搴﹀叕寮 1銆佹墖褰㈠姬闀匡細L=鍦嗗績瑙掞紙寮у害鍒讹級脳R= n蟺R/180锛埼镐负鍦嗗績瑙掞級锛圧涓烘墖褰㈠崐寰勶級2銆佹墖褰㈤潰绉細S=n蟺 R²/360=LR/...
