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Iran geometry

Source: Iranian TST 2019, third exam day 1, problem 3

April 15, 2019

geometrycircumcircle

Problem Statement

In triangle

NP

,

M,N

and

P

are midpoints of sides

BC,CA

and

AB

. Point

K

lies on segment

NP

so that

AK

bisects

\angle BKC

. Lines

MN,BK

intersects at

E

and lines

MP,CK

intersects at

F

. Suppose that

H

be the foot of perpendicular line from

A

to

BC

and

L

the second intersection of circumcircle of triangles

AKH, HEF

. Prove that

MK,EF

and

HL

are concurrent.
Proposed by Alireza Dadgarnia

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