Circular Measure (Cambridge (CIE) O Level Additional Maths): Exam Questions

The diagram shows a rectangle  and an arc  of a circle with centre at , the midpoint of .
The length of  is  and the length of  is .
Angle  is  radians.

Find the perimeter of the shape .

Find the area of the shape .

In this question all lengths are in centimetres.

The diagram shows a shaded shape. The arc  is the major arc of a circle, centre , radius 10. The line is of length 15, the line  is of length 25 and the lengths of  and  are equal.

Show that the angle  is 1.70 radians correct to 2 decimal places.

Find the perimeter of the shaded shape.

Find the area of the shaded shape.

In this question all lengths are in centimetres and all angles are in radians.

The diagram shows the rectangle , where . The points  and  lie on  such that  . The curve  is an arc of the circle, centre , radius  and has a length of .

Show that the perimeter of the shaded region is  .

Find the area of the shaded region, giving your answer in the form , where  is a constant correct to 2 decimal places.

The diagram shows an isosceles triangle  such that  and angle  radians. The points  and  lie on  and  respectively.  is an arc of length 9.6 cm of the circle, centre , radius 12 cm. The arc  touches the line  at the point .

Find the value of .

Find the total area of the shaded regions.

Find the total perimeter of the shaded regions.

The circles with centres and have equal radii of length . The line  is a radius of both circles. The two circles intersect at  and .

Given that the perimeter of the shaded region is , find the value of . [4]

Find the exact area of the shaded region.

In this question all lengths are in centimetres.

The diagram shows the figure . The arc  is part of a circle, centre , radius , and is of length . The point  lies on the straight line  such that .

Find, in radians, the angle .

Find the area of , giving your  in the form , where  is a constant.

Given that the perimeter of  is , find the value of .

The diagram shows a shape consisting of two circles of radius 3 cm and 4 cm with centres  and  which are 5 cm apart. The circles intersect at  and  as shown. The lines  and  are tangents to the circles, centres  and  respectively. Find the angle  in radians.

Find the perimeter of the whole shape.

Find the area of the whole shape.