MathDB

We are given an acute triangle

ABC

. The angle bisector of

\angle BAC

cuts

BC

P

. Points

D

and

E

lie on segments

AB

and

AC

, respectively, so that

BC \parallel DE

. Points

K

and

L

lie on segments

PD

and

PE

, respectively, so that points

A

D

E

K

L

are concyclic. Prove that points

B

C

K

L

are also concyclic.
Proposed by Patrik Bak, Slovakia

Problem Statement