问题
填空题
已知圆C：（x-2）2+（y-1）2=2，过原点的直线l与圆C相切，则所有过原点的切线的斜率之和为______．
答案
设直线方程为y=kx，即kx-y=0
圆心到直线的距离为d=
=|2k-1| k2+1 2
∴2k2-4k-1=0
∴所有过原点的切线的斜率之和为2
故答案为2．
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已知圆C：（x-2）2+（y-1）2=2，过原点的直线l与圆C相切，则所有过原点的切线的斜率之和为______．
设直线方程为y=kx，即kx-y=0
圆心到直线的距离为d=
=|2k-1| k2+1 2
∴2k2-4k-1=0
∴所有过原点的切线的斜率之和为2
故答案为2．
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