In the triangle ABC the angle bisectors AL and BT are drawn, which intersect at the point I, and their extensions intersect the circle circumscribed around the triangle ABC at the points E and D respectively. The segment DE intersects the sides AC and BC at the points F and K, respectively. Prove that:
a) quadrilateral IKCF is rhombus;
b) the side of this rhombus is DF⋅EK.(Rozhkova Maria) geometryrhombuscircumcircleincenter