20. Two semicircles are drawn in a rectangle as shown. What is the width of the overlap of the two semicircles?
A $3 \mathrm{~cm}$
B $4 \mathrm{~cm}$
C $5 \mathrm{~cm}$
D $6 \mathrm{~cm}$
E $7 \mathrm{~cm}$
20. D In the diagram, $O$ is the centre of the lower semicircle, $A$ and $C$ are the points of intersection of the two semicircles and $B$ is the point at the centre of the rectangle and also of the overlap. Now $O A$ is a radius of the semicircle so $O A$ has length $5 \mathrm{~cm}$. Also $O B$ is half the height of the rectangle so has length $4 \mathrm{~cm}$. Angle $A B O$ is a right angle. So triangle $A B O$ is a $(3,4,5)$ triangle and hence $A C=2 \times 3 \mathrm{~cm}=6 \mathrm{~cm}$.