1.14: Chord length and perimeter of a segment

0606/13/M/J/16 — Question 11 · 3 marks

The diagram shows a circle, centre

O

, radius

r\text{ cm}

. The points

A

and

B

lie on the circle such that angle

AOB = 2\theta

radians.

(i)

Find, in terms of

r

and

\theta

, an expression for the length of the chord

AB

[1]

(ii)

Given that the perimeter of the shaded region is

20\text{ cm}

, show that

r = \dfrac{10}{\theta + \sin\theta}

[2]