1 .
的外接圆与内切圆分别为
、
,
为
旁切圆.
1.证明:存在唯一圆
,
与
内切、与
外切,并且与
内切于点A.
2.设圆
与
、
的切点分别为P、Q.如果
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843d593e8cb8219aad703d77d78ef2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a8ab9c2421408d202361aca2c944fb.png)
1.证明:存在唯一圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843d593e8cb8219aad703d77d78ef2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
2.设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843d593e8cb8219aad703d77d78ef2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b746a5add435fea2d4d75c7479f01e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
您最近一年使用:0次
2 . 如图所示,在等腰
中,
,设点D是边
上一点,点E是线段
的中点,延长
与底边
交于点F,证明:若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193ea44749f1c64c8723e84a57d15cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72625fcf444310fe50db88d280bf1e81.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/99e79aad-4c4f-4957-95db-6e50f55f7ad3.png?resizew=139)
您最近一年使用:0次
3 . ⑴求证:对于任意实数x、y、z都有
.
⑵是否存在实数
,使得对于任意实数x、y、z有
恒成立?试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621d907ae622e786d2a56890cea2ad14.png)
⑵是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50eca09b66237488f8b9d9ed9737c406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c9299f308bb04438f647d975c20580.png)
您最近一年使用:0次
4 . 已知
,
.
(1)求证:
;
(2)证明:若点
在指数函数
的图像上,则对同一个
,点
也在对数函数
的图像上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d4205d528820bc28de45e4378547bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a6e2fbf26c84a3301b5249f70ac8ca.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98f2c47e43878c5ba4feb3b5cc500b9.png)
(2)证明:若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eca933e9678e98c96a35ee03e07d4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d018d0b5d1970404a82d6dc0d5e1771c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
您最近一年使用:0次
2006高三·江苏·竞赛
5 . 设 a 、b 、c 为正数 , 记 d 为(a -b)2、(b -c)2、(c -a)2 中的最小数.
(1)求证 :存在 λ(0 <λ<1),使得d ≤λ(a2 +b2 +c2);
(2)求出使不等式 ①成立的最小正数 λ,并给予证明.
(1)求证 :存在 λ(0 <λ<1),使得d ≤λ(a2 +b2 +c2);
(2)求出使不等式 ①成立的最小正数 λ,并给予证明.
您最近一年使用:0次
6 . (1)求证:正三角形各顶点到其外接圆上任一切线的距离之和为定值;
(2)猜想空间命题“正四面体各顶点到其外接球的任一切面的距离之和为定值”是否成立?证明你的结论.注:与球只有一个公共点的平面叫做球的切面,这个公共点叫做切点,切点与球心的连线垂直于切面.
(2)猜想空间命题“正四面体各顶点到其外接球的任一切面的距离之和为定值”是否成立?证明你的结论.注:与球只有一个公共点的平面叫做球的切面,这个公共点叫做切点,切点与球心的连线垂直于切面.
您最近一年使用:0次
7 . 已知数列
的前
项和为
,
且
.
(1)证明:
,并求
的通项公式;
(2)构造数列
求证:无论给定多么大的正整数
,都必定存在一个
,使
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675668080c75d532a01242ab465b411c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb8d673ef472670f69449a512cc4449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)构造数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d90b7178ae1c099f5cf8c8c9273cc04f.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/0475bd436d7637c7ad6a18e13ad66d64.png)
您最近一年使用:0次
2004高三·吉林·竞赛
8 . 设
,且
.求证:
.分析:为了证明结论中的不等式,可以先由已知条件,运用均值不等式证明以下的3个不等式
,
,
(其中
为常数).再将上述3个不等式相加即可得证.则分析过程中常数
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876060b33593f5c1981e4c300506d882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f564a7ca42b9fc2f0a21436046e06b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed65fb17fc6be31a10ae891c3485ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36cb0aa454c04efb1c44adb577d5353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf421508727cc6ec73edcde5e1eb6e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
9 . 求证:对空间不共面的任意四点
,都存在唯一的菱形
使
;若
四点共面,结论是否成立?如果成立,请给出证明;如果不成立,请举出反例.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4496fe22b40bc63581998e6b7ef6783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c5a1b05aeb2e9cc717c43c4cc411b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4496fe22b40bc63581998e6b7ef6783.png)
您最近一年使用:0次
10 . (1)求证:存在无穷多个正整数
,使得
和
同时是合数;
(2)试判断,是否存在正整数
,使得对于任意正整数
,总有
和
之一为质数?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4477c21464761f33f2868cc1a5ba793d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54ea1748b9fab39aa63880f8144d507.png)
(2)试判断,是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a550c916c64f621010e604a30ef67566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8e87146e09a898de1ba7bf63ab8eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9a5aa985e16243602f536c635cc8bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247bbb2271c2b9dd93e9844dd820728b.png)
您最近一年使用:0次