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Indonesia National Science Olympiad 2010 - Day 2 Problem 8

Source:

September 28, 2010

geometrycircumcircleratiogeometry unsolved

Problem Statement

Given an acute triangle

ABC

with circumcenter

ABC

and orthocenter

H

. Let

K

be a point inside

ABC

which is not

O

nor

H

. Point

L

and

M

are located outside the triangle

ABC

such that

AKCL

and

AKBM

are parallelogram. At last, let

BL

and

CM

intersects at

N

, and let

J

be the midpoint of

HK

. Show that

KONJ

is also a parallelogram.
Raja Oktovin, Pekanbaru

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