According to the converse of the Perpendicular Bisector Theorem, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.
In the diagram, D is equidistant from the endpoints of TC. This and the fact that DY and TC are perpendicular, mean that DY is the perpendicular bisector of TC. Therefore, we can say that TY=YC. With this, we can write an equation to find x.TY=YC⇒5x=3x+3
Let's subtract 3x on both sides to find the value of x.