MathDB

Let

AB

be a line segment with midpoint

I

. A circle, centred at

I

has diameter less than the length of the segment. A triangle

ABC

is tangent to the circle on sides

AC

and

BC

. On

AC

a point

X

is given, and on

BC

a point

Y

is given such that

XY

is also tangent to the circle (in particular

X

lies between the point of tangency of the circle with

AC

and

C

, and similarly

Y

lies between the point of tangency of the circle with

BC

and

C

. Prove that

AX \cdot BY = AI \cdot BI

Problem Statement