1. $A D$ and $B C$ are both perpendicular to $A B$, and $C D$ is perpendicular to $A C$. If $A B=4$ and $B C=3$, find $C D$.
Solution: $20 / 3$
By Pythagoras in $\triangle A B C, A C=5$. But $\angle C A D=90^{\circ}-\angle B A C=\angle A C B$, so right triangles $C A D, B C A$ are similar, and $C D / A C=B A / C B=4 / 3 \Rightarrow C D=20 / 3$.