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Two circles are tangent at F

Source: Balkan MO 2012 - Problem 1

April 28, 2012

geometrycircumcirclereflectionBMO

Problem Statement

Let

A

,

B

and

C

be points lying on a circle

\Gamma

with centre

O

. Assume that

\angle ABC > 90

. Let

D

be the point of intersection of the line

AB

with the line perpendicular to

AC

at

C

. Let

l

be the line through

D

which is perpendicular to

AO

. Let

E

be the point of intersection of

l

with the line

AC

, and let

F

be the point of intersection of

\Gamma

with

l

that lies between

D

and

E

. Prove that the circumcircles of triangles

BFE

and

CFD

are tangent at

F

.

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