### Pythagorean Triples

How many right-angled triangles are there with sides that are all integers less than 100 units?

### Tennis

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?

### Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

# A Chordingly

##### Age 11 to 14 Challenge Level:
Prove that the area of the annulus is ${1\over 4}\pi AB^2$ where $AB$ is a tangent to the inner circle.