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