MathDB

I

is the incenter of triangle

ABC

. perpendicular from

I

AI

meet

AB

and

AC

{B}'

and

{C}'

respectively . Suppose that

{B}''

and

{C}''

are points on half-line

BC

and

CB

such that

B{B}''=BA

and

C{C}''=CA

. Suppose that the second intersection of circumcircles of

A{B}'{B}''

and

A{C}'{C}''

T

. Prove that the circumcenter of

AIT

is on the

BC

Problem Statement