BG-MO 2007 Problem 1

The quadrilateral $ABCD$ , where $\angle BAD+\angle ADC>\pi$ , is inscribed a circle with centre $I$ . A line through $I$ intersects $AB$ and $CD$ in points $X$ and $Y$ respectively such that $IX=IY$ . Prove that $AX\cdot DY=BX\cdot CY$ .