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UKMT Senior Mathematical Challenge, 2018

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

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. What is the value of $\dfrac{\text{circumference of } Q + \text{circumference of } R}{\text{circumference of } P}$ ?

(A) $1$ (B) $\frac{1}{2}$ (C) $\frac{1}{3}$ (D) $\frac{1}{4}$ (E) more information needed

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