Casey s Theorem: Generalized Ptolemy s Theorem. Online College Geometry, SAT Prep

Casey's Theorem. Generalized Ptolemy's Theorem. Level: High School, SAT Prep, College geometry

In the figure below, the circles A,B,C,D are tangent to the circle O; a, b, c, d, x, y are the common tangent to circles A and B, B and C, C and D, D and A, A and C, and B and D respectively. Prove the generalized Ptolemy's theorem:
x.y = a.c + b.d

Casey Theorem, Generalized Ptolemy

See also:

4.		Ptolemy's Theorem.
3.		Cyclic Quadrilateral: Ratio of the Diagonals
2.		Brahmagupta's Theorem Cyclic quadrilateral.
1.		Quadrilaterals.