1 . 如图,
是
的内心,
的外角平分线交
于点
,直线
交
外接圆于点
,直线
与直线
交点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9020059d62af7498039f091de6f005ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c845bb8ceaa4caef3af4f1e4366b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3e927b7b2383ccded03838ae8b30b6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/f91571d9-b908-418b-9844-65875710ce74.png?resizew=220)
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2 . 定义:如果甲队赢了乙队,乙队赢了丙队,而丙队又赢了甲队,则称甲乙丙为一个“友好组”.
(1)如果19支球队参加单循环比赛,求友好组个数的最大值;
(2)如果20支球队参加单循环比赛,求友好组个数的最大值.
(1)如果19支球队参加单循环比赛,求友好组个数的最大值;
(2)如果20支球队参加单循环比赛,求友好组个数的最大值.
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3 . 已知数列
满足
,
,且
,
.
(1)证明:
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37f186bc71846ac158e74e58e42fdcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6194b7839446c93adc1b49aefb9d7214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f5f15f044af83e89e5f99565e612d6.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6eb5f27d859a1c31601425db58c885f.png)
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名校
4 . 设
是
的外心,满足
,若
,则
面积的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8954625a4411fb06322923494388b4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3354a55f2812d2e45fb70e0ff5e03be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2021-05-31更新
|
1762次组卷
|
5卷引用:2020年江苏省数学夏令营试题
2020年江苏省数学夏令营试题云南省玉溪市第一中学2019-2020学年高三上学期12月月考数学(理)试题浙江省北斗星盟2021届高三下学期5月适应性联考数学试题(已下线)2021年秋季高三数学开学摸底考试卷01(浙江专用)浙江省绍兴市诸暨市2021-2022学年高二下学期学考模拟(4)数学试题
解题方法
5 . 已知函数
.对任意
,且
,求证:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4201725a144562cc0f0da070603308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85db25f0623bb097e5a57117df267011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/400f3350d356149043b4590e2b4c8138.png)
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6 . 设k、l、c均为正整数,证明:存在正整数a、b满足
,且
,其中(a,b)表示a、b的最大公因数,
表示正整数m的所有不同正因子的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd0a2436ddb3505d7cef5937752d6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd450ba68b4f365390307deacce2b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131072b8a777616f9019dd4e4e7ce083.png)
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解题方法
7 . 已知正三棱锥P-ABC的底棱长为1,高为
,内切球的半径为r,则以内切球的球心为球心,2r为半径的球截底面三角形ABC所得图形的面积是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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8 . 证明:对任意x∈(-∞,0)∪(0,+∞),
,且等号成立的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ce5d29f74028975fb2e8bc1fe24a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a877181839d6cd64be7861712f781f06.png)
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9 . 已知椭圆
与x轴交于点A、B,过椭圆上动点M(M不与A、B重合)作椭圆的切线l,过点A、B分别作x轴的垂线,与切线l分别交于点C、D.直线CB、AD交于点Q,Q关于M的对称点为P.求点P的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5703981d2d22d4ebdd2f9369369d1b4.png)
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名校
解题方法
10 . 设
是正数数列,
,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9c167dc2de7663c031fec059996f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d4a165709c462216d1eb48ee9cceae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e18c54a4337b5987756f8bbd656638c.png)
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