MathDB

Let

ABC

be an acute triangle inscribed in a circle centered at

O

. Let

M

be a point on the small arc

AB

of the triangle's circumcircle. The perpendicular dropped from

M

on the ray

OA

intersects the sides

AB

and

AC

at the points

K

and

L

, respectively. Similarly, the perpendicular dropped from

M

on the ray

OB

intersects the sides

AB

and

BC

N

and

P

, respectively. Assume that

KL=MN

. Find the size of the angle

\angle{MLP}

in terms of the angles of the triangle

ABC

Problem Statement