MathDB

perpendicular wanted, altitudes related

Source: Moldova JBMO TST 2002 1.3

July 10, 2020

geometryperpendicularaltitudesorthocenter

Problem Statement

Let

ABC

be a an acute triangle. Points

A_1, B_1

and

C_1

are respectively the projections of the vertices

A, B

and

C

on the opposite sides of the triangle, the point

H

is the orthocenter of the triangle, and the point

P

is the middle of the segment

[AH]

. The lines

BH

and

A_1C_1

,

P B_1

and

AB

intersect respectively at the points

M

and

N

. Prove that the lines

MN

and

BC

are perpendicular.

Back to Problems View on AoPS