# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#2

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**Question**

In the diagram, OAB and OCD are radii of a circle, centre O and radius 16 cm. Angle radians. AC and BD are arcs of circles, centre O and radii 10 cm and 16 cm respectively.

**
i. **In the case where , find the area of the shaded region.

** ii. **Find the value of for which the perimeter of the shaded region is 28.9 cm.

**Solution**

From the given information we can compile following data;

** i.
**

From the given diagram it is evident that;

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

Therefore;

For ;

** ii.
**

From the given diagram it is evident that;

We know that;

Expression for length of a circular arc with radius and angle rad is;

Therefore;

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