# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#5

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**Question**

The diagram shows a semicircle with diameter AB, centre O and radius r. The point C lies on the circumference and angle AOC = radians. The perimeter of sector BOC is twice the perimeter of sector AOC. Find the value of correct to 2 significant figures.

**Solution**

We are required to find the value of angle AOC = radians.

We are given that the perimeter of sector BOC is twice the perimeter of sector AOC.

Expression for perimeter of a sector with radius and angle rad is;

Therefore;

Since AB is diameter of the semi-circle;

Hence;

Now we can write;

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