A tennis ball is served from directly above the baseline (assume
the ball travels in a straight line). What is the minimum height
that the ball can be hit at to ensure it lands in the service area?
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal can reach all points in the field. Which one is it and why?
If the sides of the triangle in the diagram are 3, 4 and 5, what is
the area of the shaded square?
This problem is taken from the UKMT Mathematical Challenges.