MathDB

AN _|_ NM wanted, AE _|_ BE, AF _|_ CF, altitude, midpoints

Source: Mathematics Regional Olympiad of Mexico Center Zone 2009 P5

November 10, 2021

perpendiculargeometry

Problem Statement

Let

ABC

be a triangle and let

D

be the foot of the altitude from

A

. Let points

E

and

F

on a line through

D

such that

AE

is perpendicular to

BE

AF

is perpendicular to

CF

, where

E

and

F

are points other than the point

D

. Let

M

and

N

be the midpoints of

BC

and

EF

, respectively. Prove that

AN

is perpendicular to

NM