1999 Cayley Problem 22

A main gas line runs through P and Q. From some point T on PQ, a supply line runs to a house at point M. A second supply line from T runs to a house at point N. What is the minimum total length of pipe required for the two supply lines?

\textbf{(A)}\ 200\quad \textbf{(B)}\ 202\quad \textbf{(C)}\ 198\quad \textbf{(D)}\ 210\quad \textbf{(E)}\ 214

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.