5. Two perpendicular chords $A C$ and $B D$ are drawn in a circle. Find the radius of the circle, given that $A B=3, C D=4$. Answer: $\frac{5}{2}$.
Solution: If we reflect $C$ across the perpendicular bisector of $B D$, we obtain a point $C^{\prime}$ on the circle such that $\angle A B C^{\prime}=90^{\circ}$, so $B C^{\prime}=C D=4,2 R=\sqrt{A B^{2}+B C^{\prime 2}}=5$.)