Here is the question:

Suppose equilateral triangle $ABC$ is inscribed in a circle. Let $P$ be on minor arc $\widehat{AB}$ such that $AP = 1$ and $BP = 3$ (lengths of the line segments). Find the distance $PC$.

Watch the recording of the class (I just fixed the incorrect link to the recording).  We spent a significant portion of the class to prove Ptolemy's Theorem.  You can try to use it for this problem.