MathDB

Let

B

and

C

be two fixed points on a circle centered at

O

that are not diametrically opposed. Let

A

be a variable point on the circle distinct from

B

and

C

and not belonging to the perpendicular bisector of

BC

. Let

H

be the orthocenter of

\triangle ABC

, and

M

and

N

be the midpoints of the segments

BC

and

AH

, respectively. The line

AM

intersects the circle again at

D

, and finally,

NM

and

OD

intersect at

P

. Determine the locus of points

P

A

moves around the circle.

Problem Statement