MathDB

Let

ABC

be an acute, non-isosceles triangle with circumcircle

(O)

BE, CF

are the heights of

\triangle ABC

, and

BE, CF

intersect at

H

. Let

M

be the midpoint of

AH

, and

K

be the point on

EF

such that

HK \perp EF

. A line not going through

A

and parallel to

BC

intersects the minor arc

AB

and

AC

(O)

P

Q

, respectively.
Show that the tangent line of

(CQE)

E

, the tangent line of

(BPF)

F

, and

MK

concur.

Problem Statement