MathDB

Let

ABC

be an acute-angled triangle in which

|AB| < |AC|

and let circle

k

with center

O

be its circumscribed circle. Let

P

and

Q

be points on sides

\overline{BC}

and

\overline{AB}

respectively such that

AQPO

is a parallelogram. Let

K

and

L

be the intersections of the perpendicular bisector of

\overline{OP}

with circle

k

, where

K

is on the shorter arc

AB

. Let

M

be the second intersection of the line

KQ

with the circle

k

. Prove that the point

A

belongs to the bisector of the angle

\angle QLM

2022.3