MathDB

Let

ABC

be a triangle with

AB \neq AC

and with incenter

I

. Let

M

be the midpoint of

BC

, and let

L

be the midpoint of the circular arc

BAC

. Lines through

M

parallel to

BI,CI

meet

AB,AC

E

and

F

, respectively, and meet

LB

and

LC

P

and

Q

, respectively. Show that

I

lies on the radical axis of the circumcircles of triangles

EMF

and

PMQ

.
Proposed by Andrew Wu

Problem Statement