设圆心为(x,y)
圆心到这3个点距离相等
(x+8)²+(y+1)²=(x-5)²+(y-12)²=(x-17)²+(y-4)²
16x+64+2y+1=-10x+25-24y+144=-34x+289-8y+16
16x+2y+65=-10x-24y+169=-34x-8y+305
{16x+2y+65=-10x-24y+169
-10x-24y+169=-34x-8y+305
解得：
{x=5
y=-1
圆心(5,-1)