Intersecting Chords Theorem and Secant-Tangent Theorem
AB is a chord passing through P on a circle. It is trivial that when P is at the center of the circle, the product of lengths PA and PB (ie. the area of the rectangle) is the same for all possible diameters AB.
a) Prove that when P is not at the center of the circle, all possible chords AB form same-area rectangles. [Hint: Move point A to consider another chord passing through P]
b) How about P is outside the circle?