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angle bisector wanted, 2 excenters related

Source: 2014 Indonesia MO Province P2 q2 OSP

December 10, 2020

geometryangle bisectorexcenter

Problem Statement

Given an acute triangle

ABC

with

AB <AC

. The ex-circles of triangle

ABC

opposite

B

and

C

are centered on

B_1

and

C_1

, respectively. Let

D

be the midpoint of

B_1C_1

. Suppose that

E

is the point of intersection of

AB

and

CD

, and

F

is the point of intersection of

AC

and

BD

. If

EF

intersects

BC

at point

G

, prove that

AG

is the bisector of

\angle BAC

.

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