MathDB

Let

ABC

be an acute triangle with

AC> AB

. be

\Gamma

the circumcircle circumscribed to the triangle

ABC

and

D

the midpoint of the smallest arc

BC

of this circle. Let

E

and

F

points of the segments

AB

and

AC

respectively such that

AE = AF

. Let

P \neq A

be the second intersection point of the circumcircle circumscribed to

AEF

with

\Gamma

. Let

G

and

H

be the intersections of lines

PE

and

PF

with

\Gamma

other than

P

, respectively. Let

J

and

K

be the intersection points of lines

DG

and

DH

with lines

AB

and

AC

respectively. Show that the

JK

line passes through the midpoint of

BC

Problem Statement