MathDB

Problem 4

Source: Azerbaijan third round 2020

June 6, 2020

geometry

Problem Statement

There is a non-equilateral triangle

ABC

.Let

ABC

's Incentri

I

.Point

D

is on the

BC

side.The circle drawn outside the triangle

IBD

and

ICD

intersects the sides

AB

and

AC

at points

E

and

F.

The circle drawn outside the triangle

DEF

intersects the sides

AB

and

AC

at

N

and

M

.Prove that

EM\parallel FN

.

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