MathDB

Iran TST

Source: Iranian TST 2019, first exam day 2, problem 4

April 10, 2019

geometry

Problem Statement

Consider triangle

ABC

with orthocenter

H

. Let points

M

and

N

be the midpoints of segments

BC

and

AH

. Point

D

lies on line

MH

so that

AC

and point

K

lies on line

AH

so that

DNMK

is cyclic. Points

E

and

F

lie on lines

AC

and

AB

such that

\angle EHM=\angle C

and

\angle FHM=\angle B

. Prove that points

D,E,F

and

K

lie on a circle.
Proposed by Alireza Dadgarnia

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