MathDB

IMO Shortlist 2009 - Problem G3

Source:

July 5, 2010

geometrysymmetryIMO ShortlistTriangleparallelogram

Problem Statement

Let

ABC

be a triangle. The incircle of

CZ

touches the sides

AB

and

AC

at the points

Z

and

Y

, respectively. Let

G

be the point where the lines

BY

and

CZ

meet, and let

R

and

S

be points such that the two quadrilaterals

BCYR

and

BCSZ

are parallelogram. Prove that

GR=GS

.
Proposed by Hossein Karke Abadi, Iran

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