求公切线的方法如果两个圆相离那么有4条公切线,分为内外,两圆间的公切线怎么求

Question

求公切线的方法
如果两个圆相离那么有4条公切线,分为内外,两圆间的公切线怎么求

Answer 1

(x1-a1)^2+(y1-b1)^2 = r1^2 -> 2(x1-a1) + 2(y-b1)*y' = 0 (1) (-1/y')(x1-a1) + b1 = y1 (2)
(x2-a2)^2+(y2-b2)^2 = r2^2 -> 2(x2-a2) + 2(y2-b2)*y' = 0 (3) (-1/y')(x2-a2) + b2 = y2 (4)
联立1,2,3,4求解y'为切线斜率,x1,y1为切点坐标,x2,y2切点坐标