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The midpoint of the altitude lies on radical axis

Source: IberoAmerican TST - Perú 2014-D02-Q02

May 11, 2015

geometrygeometry proposedpower of a pointradical axis

Problem Statement

The incircle

\odot (I)

\triangle ABC

touch

AC

and

AB

E

and

F

respectively. Let

H

be the foot of the altitude from

A

, if

R \equiv IC \cap AH, \ \ Q \equiv BI \cap AH

prove that the midpoint of

AH

lies on the radical axis between

\odot (REC)

and

\odot (QFB)

I hope that this is not repost :)