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教材上删掉的“圆幂定理”真的很好用！
初中数学合集42/138
![[初中数学]定弦定角？截长补短？三线共点？四点共圆？有趣有趣](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/5e150fadc10c419983ebed1e5aae6afb~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=xdOodLc0a%2BPFkEmH%2BxqYeJfc0fw%3D)
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App06:44![[初中数学]双动点+费马点问题：求PA+PB+PE最小值](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/3a3ec9a64dff4192962576d44c0bfe0f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=SRhzN4fTt9Ijd73QVfcos6YU9u4%3D)
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App13:16![[初中数学]三角形的三条中线为什么交于一点，三角形重心问题](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/e72d1d1b61fb45a5a771e8eda80706af~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=4vl%2FzdfjRbY1QZ7FV2VhtFSdeHI%3D)
App06:44![[初中数学]“定弦定角”+平行四边形，作完辅助线一目了然！](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/b7621026d7484fc38e24fa9b303f12c4~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=kOjCOW1uSSXS4D2MHl4ToNbQfSg%3D)
App05:09![[初中数学]那道瓜豆原理的题目居然可以用手拉手模型秒杀](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/19317f22f98c476e935fedcb5458018e~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=5hZZeYT3liC%2BryZkNWiFQnXVoqw%3D)
App05:10![[初中数学]四点共圆+角平分线，这道题这样做感觉好极了！](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/232d744684bb4116a6132d804c1f059c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=ll4044215FBCab%2FeUAjv6MpaFac%3D)
App08:27![[中考数学]平面几何''胖瘦模型''，辅助线很重要！](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/260e312ede754f5386716dc18d1ca8f9~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=zn%2BjoAMCA9buHgKHT4qKVBdrqVQ%3D)
App10:49![[初中数学]坐标系中的瓜豆原理——旋转相似很重要](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/951bf6d3f0a140229b1766a0a2b48f90~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=MKmC12RN5qLZESVfZ2ubaF9pxY8%3D)
App09:51![[初中数学]四点共圆都会了，九点共圆还远吗？](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/e93acc6cb59e4a8ca3bd0dce45350d78~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=R3rEbgUAfPcnAyW5QSDrzRvIfVQ%3D)
App07:33![[初中数学]平面几何建系法VS纯几何法，选哪个？](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/b2b066d648b84fd0bd7b34bb4bcc634a~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=zivskoIok4lwgmWfxTohfIVlh%2B4%3D)
App14:25![[初中数学]最小值求多了，来求一下线段最大值吧](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/a3bb87c498e64f4f99bb9389a95e6d41~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=8WZo1FMQ%2FHuGNprhzL1jpgacVy0%3D)
App05:10![[初中数学]求k·PA+PB+PC的最小值，加权费马点问题](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/89b3edd73d3342e3ac963769651a37f3~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=4ANFsJADGr7QDU3WKZDxDNup4aM%3D)
App06:53![[初中数学]圆周角定理中的2倍关系怎么证明？](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2053807c1e094d90b551c7967a4d8b9e~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=9sYR1bSiDeLwOhwjDJ6cgDbs39Q%3D)
App06:50![[初中数学]费马点难题警告：求3PA+4PB+5PC最小值](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/534a32ebd98c437f9144e9bf2c93d221~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=g4VMAP0d7bGp%2FscBGMrwnyWjucA%3D)
App09:53![[初中数学]全军覆没的一道最值问题，构造将军饮马很重要！](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/5619ac96344145d9a22aff820dee75ed~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=hQNKF0kMGRp9lQwndBoWXQto%2F4o%3D)
App10:08![[初中数学]垂径定理的正确打开方式，中考、高考中怎么用](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2a75c80c7b5340a3a4d4b10fde34654c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=N0BokItwmnm%2B%2B82EcQvl7yOMU0s%3D)
App11:30![[初中数学]布罗卡尔点——等腰＋相似，原来如此，相似三角形](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/71a24bd5cb8049f299d8faaeb12a4767~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=75Q%2FXwivKNcetnZurft%2FhTHgQpM%3D)
App03:31![[初中数学]加权费马点问题，为什么系数是勾股数，直击本质](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/9fe1d634810c4e70a62a7870546bd93c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=GVxWJf1KnooyLUEUrTp%2FSc020vo%3D)
App08:40![[初中数学]瓜豆原理逆运用，纯几何法解最值问题，你学废了吗？](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/93247b5a344d4f759991a1c5f6ca4dc8~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=U%2FdY1RoIjsHFiPI5bX9G%2FkFuetY%3D)
App12:36![[初中数学]平面几何辅助线怎么作？寻找题干中的蛛丝马迹](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/a69424ac6bfb4c158110b3ba46f3e585~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=u0tBxNpHOBgph0mBsOCjqi1E9co%3D)
App08:28![[初中数学]究竟是一线三垂直，还是隐形圆？代几综合](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/f815c3b7c9384029a80881cf89036987~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=GDqZV0NtY7A7AXzSys%2FxRpJZYEI%3D)
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App08:40![平面几何中的“海盗埋宝”模型[初中数学]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/6ad865d4be814ab7b2a5b68568475f3c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=a15SIOiggoECvvWFPuVR3GTftNY%3D)
App08:51![[中考数学]反向手拉手模型](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/fd44fd2e075b4ef4a588a06d171801cb~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=Qgpr9k9SyYW7X4M0yTvPufYOeL8%3D)
App09:39![[中考数学]平面几何模型——中点四边形模型](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/7b78bc4dfbb64bdda49ee7b338068a23~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=2025043012414565123FA75CED26CA5459&requestFrom=704&version_code=80402&x-expires=1777524105&x-signature=5ulQ94ecTgOKlMchjCRdq4PtXMA%3D)
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