Width of a pond from ground measurements

A gardener wants the distance \(AB\) across a pond. She chooses a point \(C\) on open ground, walks from \(A\) through \(C\) to \(D\) so that \(CD=AC\), and from \(B\) through \(C\) to \(E\) so that \(CE=BC\).

1. Prove that \(DE=AB\).[4]
2. She measures \(DE=23.4\) m. State one assumption needed for \(23.4\) m to be the width of the pond.[1]
3. Her friend uses less ground: he marks the midpoints \(P\) of \(AC\) and \(Q\) of \(BC\), and measures \(PQ=11.6\) m. Prove that \(AB=2PQ\), find \(AB\), and comment on the two results.[3]