level of difficulty: 3/5
Here is a general representation of the problem:
steps:
1. when distance between T and i is bigger than a fixed size -
2. figure out the angle, better yet the radian between T (touched point) and i and the point straight line that crosses the circle horizontally.
3. then find the sizes of the adjacent and opposite sides of the triangle in the circle by finding: cos/sin(radian)max_radius
4. then, depending on which quarter we are talking about, I will either subtract or add , opposite to Yi and adjacent to Xi to get P(x, y) and also keep in mind the width/2f and height/2f so that the coordinates of P are exactly the middle of the ball.
