If the base of a rectangle is increased by 10% and the area is
unchanged, by what percentage (exactly) is the width decreased by ?
Equal circles can be arranged so that each circle touches four or
six others. What percentage of the plane is covered by circles in
each packing pattern? ...
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
This problem is taken from the UKMT Mathematical Challenges.