Ptolemy theorem
"If a quadrilateral is inscribable in a circle then the product of the measures of its diagonals
is equal to the sum of the products of the measures of the pairs of opposite sides".
Proof:
1. sin(β) = sin(π-α) = sin(α)
2. 2P = 2(P1+P2+P3+P4) = x1y1sin(α)+y1x2sin(β)+x2y2sin(α)+y2x1sin(β) =
(x1y1+y1x2+x2y2+y2x1)sin(α) = (x1+x2)(y1+y2)sin(α) = xysin(α)
3. 2P = 2(P6+P7) = acsin(β)+bdsin(α) = (ac+bd)sin(α)
4. xy = ac+bd