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Romania Junior TST 2021 Day 1 P3

Source:

May 16, 2021

geometryincenterRomanian TSTTST

Problem Statement

The incircle of triangle

ABC

is tangent to the sides

AB,AC

and

BC

at the points

M,N

and

I

respectively. The median

ABC

of the triangle

ABC

intersects

MN

at the point

L

. Prove that

K,I

and

L

are collinear, where

I

is the incenter of the triangle

ABC

.

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