MathDB

perpendicular wanted, orthocenter, circumcenter, midpoints related

Source: 2015 Saudi Arabia GMO TST I p3

August 1, 2020

geometryorthocenterCircumcenterperpendicular

Problem Statement

Let

BD

and

CE

be altitudes of an arbitrary scalene triangle

ABC

with orthocenter

H

and circumcenter

O

. Let

M

and

N

be the midpoints of sides

AB

, respectively

AC

, and

P

the intersection point of lines

MN

and

DE

. Prove that lines

AP

and

OH

are perpendicular.
Liana Topan