MathDB

Let

ABC

be an acute triangle and let

X

and

Y

be points on the segments

AB

and

AC

such that

BX = CY

. If

I_{B}

and

I_{C}

are centers of inscribed circles in triangles

ABY

and

ACX

, and

T

is the second intersection point of the circumcircles of

ABY

and

ACX

, show that:

\frac{TI_{B}}{TI_{C}} = \frac{BY}{CX}.

Proposed by Nikola Velov

Problem Statement