MathDB

Circle geo

Source: BMO Shortlist 2022, G5

May 13, 2023

geometry

Problem Statement

Let

ABC

be a triangle with circumcircle

\omega

, circumcenter

O{}

, and orthocenter

H{}

. Let

K{}

be the midpoint of

AH{}

. The perpendicular to

OK{}

at

K{}

intersects

AB{}

and

AC{}

at

P{}

and

Q{}

, respectively. The lines

BK

and

CK

intersect

\omega

again at

X{}

and

Y{}

, respectively. Prove that the second intersection of the circumcircles of triangles

KPY

and

KQX

lies on

\omega

.
Stefan Lozanovski

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