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Iranian geometry olympiad 2014(2)

Source: Iranian geometry olympiad 2014

February 22, 2015

geometryanalytic geometrygraphing linesslopeparallelogramsymmetrygeometry proposed

Problem Statement

Two points

P

and

Q

lying on side

BC

of triangle

ABC

and their distance from the midpoint of

BC

are equal.The perpendiculars from

P

and

Q

to

BC

intersect

AC

and

AB

at

E

and

F

,respectively.

M

is point of intersection

PF

and

EQ

.If

H_1

and

H_2

be the orthocenters of triangles

BFP

and

CEQ

, respectively, prove that

AM\perp H_1H_2

.
Author:Mehdi E'tesami Fard , Iran

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