MathDB

Let

ABC

be an acute triangle with

AC > AB

. Let

\Gamma

be the circle circumscribed to the triangle

ABC

and

D

the midpoint of the smaller arc

BC

of this circle. Let

I

be the incenter of

ABC

and let

E

and

F

be points on sides

AB

and

AC

, respectively, such that

AE = AF

and

I

lies on the segment

EF

. Let

P

be the second intersection point of the circumcircle of the triangle

AEF

with

\Gamma

with

P \ne A

. Let

G

and

H

be the intersection points of the lines

PE

and

PF

with

\Gamma

different from

P

, respectively. Let

J

and

K

be the intersection points of lines

DG

and

DH

with lines AB and

AC

, respectively. Show that the line

JK

passes through the midpoint of

BC

Problem Statement