Ptolemy Theorem

Terry Tam
ABCD is a cyclic quadrilateral. a) A and A' are the inversion points of each other. Prove that and b) Applying result of a) on B and C (their corresponding inversion points are B' and C' with the same inversion circle), prove that and express B'C' in terms of r and sides of . c) Applying the above results to another two triangles, prove the Ptolemy Theorem.