Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.
Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.
A cyclist and a runner start off simultaneously around a race
track each going at a constant speed. The cyclist goes all the way
around and then catches up with the runner. He then instantly turns
around and heads back to the starting point where he meets the
runner who is just finishing his first circuit. Find the ratio of
This is an unusual question in that you are given no numerical
information but have to find a numerical answer.