Online Geometry, Theorems and Problems

Geometry Problem 1206: Circle, Angle Bisector, Secant, Triangle, Circumcircle, Congruence, Area. Online High School, College.

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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.
  

See also:
Triangles
Angle Bisector
Congruence
Circle

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Last updated: Apr 9, 2016