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Two incenters on a parallel line

Source: Mexican Math Olympiad 2012 - problem 6

December 1, 2013

geometryincentercircumcirclegeometry unsolved

Problem Statement

Consider an acute triangle

ABC

with circumcircle

\mathcal{C}

. Let

H

be the orthocenter of

ABC

and

M

the midpoint of

BC

. Lines

AH

,

BH

and

H

cut

\mathcal{C}

again at points

D

,

E

, and

F

respectively; line

MH

cuts

DFJ

at

J

such that

H

lies between

J

and

M

. Let

K

and

L

be the incenters of triangles

DEJ

and

DFJ

respectively. Prove

KL

is parallel to

BC

.

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