Do you see that the center of the two circles is at (2, 2) and (10, 8)? And since they have the same radius, the situation is symmetric: the belts cross at . If (a, b) is the point where the first touches the second circle, the slope of the line from (6, 5) to (a, b) is . Also, the slope of the line from the center of that circle to (a, b) is . Since those two lines must be perpendicular, it must be true that their product is -1: . That gives you one equation in a and b. Since (a, b) is on the second circle, you also have . You can solve those two equations for a and b.