MathDB

Rhombus formed with circumcenter and orthocenter

Source: Problem 7 of Russian Regional Olympiad 2011, grade 10

September 1, 2011

geometryrhombuscircumcircleangle bisectorgeometry proposed

Problem Statement

Points

C_0

and

B_0

are the respective midpoints of sides

AB

and

AC

of a non-isosceles acute triangle

ABC

O

is its circumscenter and

H

is the orthocenter. Lines

BH

and

OC_0

intersect at

P

, while lines

CH

and

OB_0

intersect at

Q

OPHQ

is rhombus. Prove that points

A

P

and

Q

are collinear. (Author: L. Emelyanov)