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Iran geometry

Source: Iran MO 3rd round 2017 mid-terms - Geometry P3

August 10, 2017

geometry

Problem Statement

Let

ABC

be an acute-angle triangle. Suppose that

M

be the midpoint of

BC

and

H

be the orthocenter of

ABC

. Let

F\equiv BH\cap AC

and

E\equiv CH\cap AB

. Suppose that

X

be a point on

EF

such that

\angle XMH=\angle HAM

and

A,X

are in the distinct side of

MH

. Prove that

AH

bisects

MX

.

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