CONO-SUR 2002 Problem 2

Given a triangle $ABC$ , with right $\angle A$ , we know: the point $T$ of tangency of the circumference inscribed in $ABC$ with the hypotenuse $BC$ , the point $D$ of intersection of the angle bisector of $\angle B$ with side AC and the point E of intersection of the angle bisector of $\angle C$ with side $AB$ . Describe a construction with ruler and compass for points $A$ , $B$ , and $C$ . Justify.