3.28: Intersecting circles with mutual tangents at contact points

0606/12/O/N/24 — Question 3 · 7 marks

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

The diagram shows a circle with centre

O

and radius

12

, and a circle with centre

C

and radius

5

The circles intersect at the points

A

and

B

, such that

OA

and

OB

are tangents to the circle with centre

C

(a)

Show that the obtuse angle

ACB

2.35

radians, correct to

2

decimal places.

[2]

(b)

Find the perimeter of the shaded region.

[2]

(c)

Find the area of the shaded region.

[3]