MathDB

Concurrence of angle bisectors

Source: Brazil MO #5

October 20, 2011

geometrycircumcircletrigonometryparallelogramBrazilian Math OlympiadHarmonic Quadrilateral

Problem Statement

Let

ABC

be an acute triangle and

H

is orthocenter. Let

D

be the intersection of

BH

and

AC

and

E

be the intersection of

CH

and

AB

. The circumcircle of

ADE

cuts the circumcircle of

ABC

F \neq A

. Prove that the angle bisectors of

\angle BFC

and

\angle BHC

concur at a point on

BC.