名校
解题方法
1 . 如图,在平面直角坐标系中,一次函数
与坐标轴交于点A,B,点C为
上一动点,过点C作
于点D,过点D作
轴,交y轴于点E,在直线
上找一点F,使得
,连接
,当
的值最小时,求点F的坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca621dc42304f844ac15dad7062d3959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a880ffabfdf4a3ae2226616d80f08d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc60f2fd9c91293a743111539202a169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c88c0a51e576069b649e71df535ce5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 如图,在矩形
中,
分别与
相切于
三点,过点
作
的切线交
于点
,切点为
,则
的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/330a06fe73b52d1b90194b1a0d2d92e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/27/b9d68d6f-9d59-4446-91d1-311955fb0e57.png?resizew=157)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024高三·全国·专题练习
3 . 如图,在
中,O是外心,D是BC边的垂足.设
的外接圆与
的九点圆交于X、Y两点.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7ffcd1925a2b1259221c6a476152f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51bb929a401607ea5758a8e409b9583.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/980086bc-f3de-4339-98d1-14202dac7c5c.png?resizew=149)
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4 . 如图,在平行四边形ABCD中,
,分别以A,C为圆心,大于
的长为半径画弧,两弧相交于点M,N,过M,N两点作直线,与
交于点E,与
交于点F,连接AE,CF,则四边形
的周长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb2b9021643004444e48bfe8f344448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93148adbc6e856da9a9d263f485d003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910936ec9fb419d51ce2f5ea817f8401.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/67e511b5-298d-46f3-a65e-e11cf97a0408.png?resizew=220)
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5 . 如图,锐角
内接于
的平分线交AC于点D,连接 DO并延长交AB于点E,设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/8cdd39cf-044f-4efe-ad14-91463381491a.png?resizew=147)
(1)当
时,求证:
;
(2)当
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce243143b38fe2de91f3d307564c89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ef05f8d2b1822559d84b70f05993a1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/8cdd39cf-044f-4efe-ad14-91463381491a.png?resizew=147)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c436f108fd4921dae15ecff19270237e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5181b97a7e43959b8455680157c3b644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6 . 在
中,
,过
的内切圆圆心I作
,分别与AB,AC相交于点D,E.则DE的长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a768ecc913c5f0cd0f8b436ee489bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c436f108fd4921dae15ecff19270237e.png)
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7 . 在锐角
中,
为
延长线上一点,过
分别作
,
平行线
,
,若
,
,且
的外接圆与
交于点
,证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5161dac60a307b5768018875063deaac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d61be62a066c7ad65f9fa64ba1de1ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d172d77168b66134a5a852412d4f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6af45c7f8453cf711317ffe66dccec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345f52e0835cc13f92b6801169105a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4c6b0869d7248b6c2f964718a67702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0424af44604f489a804efb1e4b28a0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940730a19110cc363c871e0599388e56.png)
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2023-12-14更新
|
154次组卷
|
2卷引用:2023年第39届全国中学生冬令营(CMO)数学试题
8 . 已知点,过点
的直线
上有一个动点
,则
的最小值为
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2023高三·全国·专题练习
9 . 如图所示,菱形
的对角线
与
交于点
,点
、
分别为
、
的中点,
交
于点
,将
沿
折起到
的位置.
;
(2)若
,
,
,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e8bb1e2dbfd5c00e6a5432bb288265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d155087b35835c45b87649ac73a9412.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a566b100fb2ebe3d208f9b6527934218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01cd2bf7c88e24c91625e0f20ba2a4bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7922e202f2cfaae7280d214421501c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6b669ae31b8b0813948d106c942a9e.png)
您最近一年使用:0次
10 . 如图,
是以
为直径的固定的半圆弧,
是经过点
及
上另一个定点
的定圆,且
的圆心位于
内.设
是
的弧
(不含端点)上的动点,
,
是
上的两个动点,满足:
在线段
上,
,
位于直线
的异侧,且
.记
的外心为
.证明:
(1)点
在
的外接圆上;
(2)
为定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8059a935a2325a9e7abbcbf56aa167f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f4ee45d9bfe4281d0501e0729b7ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96645a3530e72d5d733d2c72147d340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/17/e92a7992-52b6-406b-8d62-a94eb3bfd8ee.png?resizew=177)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9705bb0595ad62312a40b99e4d31139e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
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