You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter) exactly $4\times$ as fast as you can row, and he will always run towards the closest bit of shore to you. If you can touch shore even for a second without the monster already being upon you, you can escape. Suggest a strategy that will allow you to escape, and prove that it works.
- If two paths take the monster to this location equally quickly, he will arbitrarily choose one.
- The monster can reverse direction instantaneously, and you can turn your boat instantaneously.
Follow up: What is the minimum speed of the monster (relative to your boat) such that escape becomes impossible?