MathDB

Let

ABC

be a scalene acute-angled triangle with its incenter

I

and circumcircle

\Gamma

. Line

AI

intersects

\Gamma

for the second time at

M

. Let

N

be the midpoint of

BC

and

T

be the point on

\Gamma

such that

IN \perp MT

. Finally, let

P

and

Q

be the intersection points of

TB

and

TC

, respectively, with the line perpendicular to

AI

I

. Show that

PB = CQ

. Proposed by Patrik Bak - Slovakia

Problem Statement