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Cyclic Quadrilateral

Source: Problem 2, Centroamerican Olympiad 2009

October 7, 2009

geometrygeometric transformationhomothetyreflectioncyclic quadrilateralpower of a pointradical axis

Problem Statement

\item Two circles

\Gamma_1

and

\Gamma_2

intersect at points

A

and

B

. Consider a circle

\Gamma

contained in

\Gamma_1

and

\Gamma_2

, which is tangent to both of them at

D

and

G

respectively. Let

DC

be one of the intersection points of line

AB

with

\Gamma

,

F

be the intersection of line

EC

with

\Gamma_2

and

G

be the intersection of line

DC

with

\Gamma_1

. Let

H

and

I

be the intersection points of line

ED

with

\Gamma_1

and

\Gamma_2

respectively. Prove that

F

,

G

,

H

and

I

are on the same circle.

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