MathDB

In triangle

ABC

(\angle A\neq 90^\circ)

, let

O

H

be the circumcenter and the foot of the altitude from

A

respectively. Suppose

M

N

are the midpoints of

BC

AH

respectively. Let

D

be the intersection of

AO

and

BC

and let

H'

be the reflection of

H

about

M

. Suppose that the circumcircle of

OH'D

intersects the circumcircle of

BOC

E

. Prove that

NO

and

AE

are concurrent on the circumcircle of

BOC

.
Proposed by Mehran Talaei

Problem Statement