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2014 China Second Round Olympiad Second Part Problem 2

Source: 2014 China Second Round Olympiad

August 4, 2015

geometrycircumcircle

Problem Statement

Let

ABC

be an acute triangle such that

\angle BAC \neq 60^\circ

. Let

D,E

be points such that

BD,CE

are tangent to the circumcircle of

F,G

and

BD=CE=BC

(

A

is on one side of line

BC

and

D,E

are on the other side). Let

F,G

be intersections of line

DE

and lines

AB,AC

. Let

M

be intersection of

CF

and

BD

, and

N

be intersection of

CE

and

BG

. Prove that

AM=AN

.

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