The figure shows a circle O and
of an angle AMB (A and B on circle O). P is a point on LM extended, lines PBC and PAD are
secants to circle O. AM and BM extended cut the circumcircles of triangles PMB
and PMA at R and Q, respectively. Prove that (1) AR = BQ; (2)
Area of triangle PDQ = Area of triangle PCR.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.