MathDB

Perpendicular

Source: APMO 1998

March 17, 2006

geometrycircumcirclerectangleAPMO

Problem Statement

Let

ABC

be a triangle and

D

the foot of the altitude from

A

. Let

E

and

F

lie on a line passing through

D

such that

AE

is perpendicular to

BE

,

AF

is perpendicular to

CF

, and

E

and

F

are different from

D

. Let

M

and

N

be the midpoints of the segments

BC

and

EF

, respectively. Prove that

AN

is perpendicular to

NM

.

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