## Task B-3.3.

A right triangle $A B C$ is given with a right angle at vertex $C$ and a hypotenuse of length $6 \mathrm{~cm}$. On the hypotenuse $\overline{A B}$, point $P$ is marked, and on the leg $\overline{B C}$, point $Q$ is marked such that $|B P|=|Q C|=1 \mathrm{~cm}$. If $\varangle B P Q=90^{\circ}$, determine $|P C|$.