怎样求两圆外公切线的交点?如题.两圆圆心坐标为O1(x1,y1),O2(x2,y2)两圆的半径为r1,r2.求外公切线的坐标.请给出推理或者计算过程,

Question

怎样求两圆外公切线的交点?
如题.
两圆圆心坐标为O1(x1,y1),O2(x2,y2)
两圆的半径为r1,r2.
求外公切线的坐标.
请给出推理或者计算过程,

Answer 1

假设外公切线的交点是M,且r1≥r2
则外公切线的交点在圆心的连线上,
利用几何特点：r1/r2= O1M/O2M
O1M=O1O2 + O2M
(r1-r2)/r2= O1O2/O2M
O2M = O1O2*r2/(r1-r2)
M点坐标：(x-x2) /(x2-x1)= O2M /O1O2
x= O2M*(x2-x1)/O1O2 +x2
= O1O2 *r2/(r1-r2)*(x2-x1)/O1O2 + x2
= r2/(r1-r2)*(x2-x1) + x2
同理：y= r2/(r1-r2)*(y2-y1) +y2