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perpendicularity starting with a rectangle, danube junior 2013

Source: Danube 2013 Junior P4

September 7, 2018

geometryrectangleperpendicular

Problem Statement

Let

ABCD

be a rectangle with

AB \ne BC

and the center the point

O

. Perpendicular from

O

BD

intersects lines

AB

and

BC

in points

E

and

F

respectively. Points

M

and

N

are midpoints of segments

[CD]

and

[AD]

respectively. Prove that

FM \perp EN