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AKOM is a paralleogram - JBMO Shortlist

Source:

October 30, 2010

geometryparallelogramgeometry proposed

Problem Statement

Consider the triangle

ABC

with

\angle A= 90^{\circ}

and

\angle B \not= \angle C

. A circle

E

passes through

B

and

C

and intersects the sides

AB

and

AC

at

D

and

E

, respectively. Let

S

be the foot of the perpendicular from

A

to

BC

and let

K

be the intersection point of

AS

with the segment

DE

. If

M

is the midpoint of

BC

, prove that

AKOM

is a parallelogram.

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