13. Let $A B$ and $C D$ be perpendicular segments intersecting at point $P$. Suppose that $A P=2$, $B P=3$ and $C P=1$. If all the points $A, B, C, D$ lie on a circle, find the length of $D P$.
13. Answer: 6.

Since $\angle A=\angle D$ and $\angle C=\angle B$, the triangles $\triangle A C P$ and $\triangle D B P$ are similar. Then
$$
\frac{D P}{B P}=\frac{A P}{C P} \Rightarrow D P=\frac{A P}{C P} \times B P=\frac{2}{1} \times 3=6 .
$$