MathDB

Let

ABC

be a triangle and let

P

be a point on the angle bisector

AD

, with

D

BC

. Let

E

F

and

G

be the intersections of

AP

BP

and

CP

with the circumcircle of the triangle, respectively. Let

H

be the intersection of

EF

and

AC

, and let

I

be the intersection of

EG

and

AB

. Determine the geometric place of the intersection of

BH

and

CI

when

P

varies.

Problem Statement