MathDB

In the isosceles triangle

ABC

where

AB = AC

, the point

I{}

is the center of the inscribed circle. Through the point

A{}

all the rays lying inside the angle

BAC

are drawn. For each such ray, we denote by

X{}

and

Y{}

the points of intersection with the arc

BIC

and the straight line

BC

respectively. The circle

\gamma

passing through

X{}

and

Y{}

, which touches the arc

BIC

at the point

X{}

is considered. Prove that all the circles

\gamma

pass through a fixed point.

Problem Statement