The figure shows a circle O and
bisector ML
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.
![Geometry Problem 1206: Circle, Angle Bisector, Secant, Triangle, Circumcircle, Congruence, Area.](p1206-circle-angle-bisector-secant-congruence-area.gif)
See
also:
Triangles
Angle Bisector
Congruence
Circle
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