Ptolemy's Theorem GMM 2f
Ptolemy's theorem states that when a quadrilateral is inscribed in a circle and the diagonals of that quadrilateral are drawn, the product of the diagonals is equal to the product of two opposite sides of the quadrilateral plus the product of the other two sides. This means that CE*DF=(CF*DE)+(FE*CD).
1) What happens when the diagonals meet in the center of the circle? What shape is created? 2) What happens when the quadrilateral created is a trapezoid? How is the shaded area affected? 3) Is it possible for the quadrilateral to turn into a right triangle? If so, is it still applicable to the theorem?