MathDB

5

Part of 2011 Brazil National Olympiad

Problems(1)

Concurrence of angle bisectors

Source: Brazil MO #5

10/20/2011
Let ABCABC be an acute triangle and HH is orthocenter. Let DD be the intersection of BHBH and ACAC and EE be the intersection of CHCH and ABAB. The circumcircle of ADEADE cuts the circumcircle of ABCABC at F≠AF \neq A. Prove that the angle bisectors of ∠BFC\angle BFC and ∠BHC\angle BHC concur at a point on BC.BC.
geometrycircumcircletrigonometryparallelogramBrazilian Math OlympiadHarmonic Quadrilateral