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Iranian geometry olympiad 2014(4)

Source: Iranian geometry olympiad 2014

February 25, 2015

geometryIran

Problem Statement

Let

ABC

be an acute triangle.A circle with diameter

BC

meets

AB

and

AC

at

E

and

F

,respectively.

M

is midpoint of

BC

and

P

is point of intersection

AM

with

EF

.

X

is an arbitary point on arc

EF

and

Y

is the second intersection of

XP

with a circle with diameter

BC

.Prove that

\measuredangle XAY=\measuredangle XYM

. Author:Ali zo'alam , Iran

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