Problem 3. Points $A$ and $B$, located on a circular avenue, are connected by a straight highway segment 4 km long, which is the diameter of the circular avenue. A pedestrian left his house and started walking along the avenue from point $A$. After 1 hour, he realized he had forgotten his keys and asked a neighbor-cyclist to bring them as quickly as possible. What is the minimum time it will take for the pedestrian to receive the keys if the cyclist's speed on the highway is 15 km/h, on the avenue - 20 km/h, and the pedestrian's speed is 7 km/h? The pedestrian can walk towards the cyclist.
Answer: after $\frac{4 \pi-7}{27}$ hours.

Solution. For definiteness, let's assume that the pedestrian went for a walk along the circular alley counterclockwise. At point $A$, the cyclist has three options: