MathDB

Sharygin CR 2019 P20

Source: Sharygin CR 2019 P20 (Grade 10 - 11)

March 6, 2019

geometry

Problem Statement

Let

O

be the circumcenter of triangle ABC,

H

be its orthocenter, and

M

be the midpoint of

AB

. The line

MH

meets the line passing through

O

and parallel to

AB

at point

K

lying on the circumcircle of

ABC

. Let

P

be the projection of

K

onto

AC

. Prove that

PH \parallel BC

.

Back to Problems View on AoPS