MathDB

Let

{I}

be the incenter of

\triangle {ABC}

and

{BX}

{CY}

are its two angle bisectors.

{M}

is the midpoint of arc

\overset{\frown}{BAC}

. It is known that

MXIY

are concyclic. Prove that the area of quadrilateral

MBIC

is equal to that of pentagon

BXIYC

.
Proposed by Dominik Burek - Poland

Problem Statement