7. The circles $P, Q$ and $R$ are all tangent to each other. Their centres all lie on a diameter of $P$, as shown in the figure.
$$
\text { What is the value of } \frac{\text { circumference of } Q+\text { circumference of } R}{\text { circumference of } P} \text { ? }
$$

A 1
B $\frac{1}{2}$
C $\frac{1}{3}$
D $\frac{1}{4}$

E more information needed
Solution
A
Let the radius of the circle $Q$ be $q$ and the radius of the circle $R$ be $r$. We see that the diameter of the circle $P$ is $2 q+2 r$ It follows that the radius of $P$ is $q+r$.

We now use the formula
$$
\text { circumference }=2 \pi \times \text { radius, }
$$
to deduce that
$$
\begin{array}{l}
\frac{\text { circumference of } Q+\text { circumference of } R}{\text { circumference of } P}=\frac{2 \pi q+2 \pi r}{2 \pi(q+r)} \\
=\frac{2 \pi(q+r)}{2 \pi(q+r)} \\
=1 \\
\end{array}
$$