Below is a question and the intended solution to a math contest problem.
I understand that if for both circles, if you assume that a circle's centre, the two points on the circumference that touch a tangent line each, and the intersection of the tangent lines; that these four points form a square, then the distances can be calculated trivially.
Thus, I would like to know how it is known that the points form two squares.
To clarify, this is what I would like to know:
Given a circle and two perpendicular lines both tangent to the circle, how is it known that the tangent points + center + intersection point forms a square?