2.4: Composite shape from two intersecting circles

0606/21/O/N/20 — Question 12 · 10 marks

The diagram shows a shape consisting of two circles of radius

3\text{ cm}

and

4\text{ cm}

with centres

A

and

B

which are

5\text{ cm}

apart. The circles intersect at

C

and

D

as shown. The lines

AC

and

BC

are tangents to the circles, centres

B

and

A

respectively.

(a)

Find the angle

CAB

in radians.

[2]

(b)

Find the perimeter of the whole shape.

[4]

(c)

Find the area of the whole shape.

[4]