MathDB

Let the side

AC

of triangle

ABC

touch the incircle and the corresponding excircle at points

K

and

L

respectively. Let

P

be the projection of the incenter onto the perpendicular bisector of

AC

. It is known that the tangents to the circumcircle of triangle

BKL

K

and

L

meet on the circumcircle of

ABC

. Prove that the lines

AB

and

BC

touch the circumcircle of triangle

PKL

Problem Statement