MathDB

Let

I

be the incenter of a triangle

ABC

. The lines passing through

A

and parallel to

BI, CI

meet the perpendicular bisector to

AI

at points

S, T

respectively. Let

Y

be the common point of

BT

and

CS

, and

A^*

be a point such that

BICA^*

is a parallelogram. Prove that the midpoint of segment

YA^*

lies on the excircle of the triangle touching the side

BC

Problem Statement