12

Part of 2001 JBMO ShortLists

Problems(1)

AKOM is a paralleogram - JBMO Shortlist

Source:

Consider the triangle

ABC

\angle A= 90^{\circ}

\angle B \not= \angle C

\mathcal{C}(O,R)

B

C

and intersects the sides

AB

AC

D

E

, respectively. Let

S

be the foot of the perpendicular from

A

BC

K

be the intersection point of

AS

with the segment

DE

M

is the midpoint of

BC

AKOM

is a parallelogram.

geometryparallelogramgeometry proposed