Extra Proplem 7 Ptolemy s theorem Let ABCD be a cyclic quadrilateral a quadri lateral whose vertices lie on a common circle Show that AC BD AB CD BC AD Hint After you draw the diagonals you should see a lot of triangles and many pairs of congruent inscribed angles There are many ways to proceed here The sine theorem should be useful along with some trig identities Have patience with this one B As we have seen many special triplets of lines in a triangle are concurrent The