Consider a circle O with a diameter AB, shown here in green. Draw a second circle (red) with diameter AC, such that C is on AB. Draw an isosceles triangle with base CB and third vertex D on circle O. Draw a third circle (X), tangent to the first three figures. Prove that the line from C to the center of circle X is perpendicular to AB.
First, draw the diagram on a sheet of paper. Add a new point E as the center of AB. This is the center of the big circle. Then add point F as the center of AC. This is the center of the medium circle. Connect F to X and label the tangent of the two circles as G. Next add H as the tangent between the circle X and the triangle.
Now connect X to H and realize the obvious that CHX is a right triangle. Look at the diagram for 60 minutes, and then type in the results. Next step: Sit back and wait for someone who remembers all of their geometry to post a comment.
Thats what I did.