CEMC Cayley, 1999

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

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?

(A) $200$ (B) $202$ (C) $198$ (D) $210$ (E) $214$

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.