Circles Intersecting

Question

If I have a circle A and a circle B, and they are intersecting, how can I find the point along circle A's circumference that is closest to the center of circle B knowing the radius and x and y position of both circle A and B?

Answer 1

Circle A:
(x-Xa)^2 + (y-Ya)^2 = Ra^2 --> center at (Xa,Ya) with radius Ra

Circle B:
(x-Xb)^2 + (y - Yb)^2 = Rb^2 ---> center at (Xb,Yb) with radius Rb



(x-Xa)^2 + (Yb-Ya)^2 = Ra^2

(x-Xa)^2 = Ra^2 - (Yb-Ya)^2

x-Xa = square root ( Ra^2 - (Yb-Ya)^2 )

x = square root( Ra^2 - (Yb - Ya)^2 ) + Xa

Answer 2

No matter what, the point shall be in the line joining the two centers.

Convince yourself by drawing several random examples.