In right \triangle A B C, P and Q are on legs B C and A C, respectively, such that C P= C Q=20. Through the point of intersection, R, of A P and B Q, a line is drawn also passing through C and meeting the hypotenuse A B at S. The extension of P Q meets line A B at T. Suppose A B=100, and A C=80. Then, if the length of T S is k, find k.