This materials shows that line PQ is always tangent to the circle at G. Move the point P to see that angle OGP is always equal to 90 degree.
Details:
[list]
[*]F and E are midpoints of the sides of the square ABCD.
[*]AP and FQ are parallel.
[*]FE (not shown) is the diameter of the circle and is equal to AB.
[*]G is the point of tangency of the circle and the line PQ.
[/list]
A problem in geometry requires to analytically prove that PQ is always tangent to the circle.
