MathDB

A circle inscribed in an angle with vertex

O

touches its sides at points

A

and

B

K

is an arbitrary point on the smaller of the two arcs

AB

of this circle. On the line

OB

a point

L

is taken such that the lines

OA

and

KL

are parallel. Let

M

be the intersection point of the circle

\omega

circumscribed around triangle

KLB

, with line

AK

, with

M

different from

K

. Prove that line

OM

touches circle

\omega

Problem Statement