Q:

How to find point on a circle that's opposite another point?

How do I find the coordinate of point and angle value on circle sprite which placed on opposite side of sprite from a touch point and the center point of the sprite?
I know A position, B position and sprite circle size. How do I calculate the position of C? and the angle it is around the sprite circle?

A:

Calculate a vector from B to A, normalize it (divide by the vector's length), then multiply by the circle size:
vx = A.x - B.x
vy = A.y - B.y
length = sqrt(vx*vx + vy*vy)
C.x = vx / length * size + A.x
C.y = vy / length * size + A.y

For the angle you can use the atan2 function, if your language has it.

A:

to complete the answer:
angle = atan2((C-A).y, (C-A).x) + PI/2;

