MathDB

Let

ABC

be a triangle with incentre

I

and circumcircle

\omega

. Let

D

and

E

be the second intersection points of

\omega

with

AI

and

BI

, respectively. The chord

DE

meets

AC

at a point

F

, and

BC

at a point

G

. Let

P

be the intersection point of the line through

F

parallel to

AD

and the line through

G

parallel to

BE

. Suppose that the tangents to

\omega

A

and

B

meet at a point

K

. Prove that the three lines

AE,BD

and

KP

are either parallel or concurrent.
Proposed by Irena Majcen and Kris Stopar, Slovenia

Problem Statement