TW-TST 2002 Problem 6

Let $A,B,C$ be fixed points in the plane , and $D$ be a variable point on the circle $ABC$ , distinct from $A,B,C$ . Let $I_{A},I_{B},I_{C},I_{D}$ be the Simson lines of $A,B,C,D$ with respect to triangles $BCD,ACD,ABD,ABC$ respectively. Find the locus of the intersection points of the four lines $I_{A},I_{B},I_{C},I_{D}$ when point $D$ varies.