Why is the area of rectangles always the same?
- Terry Tam
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. Prove that when P is not at the center of the circle, all possible chords AB form same-area rectangles. How about P is outside the circle? [Hint: Move point A to consider another chord passing through P]