Long Questions (Question 4)

Diagram below shows two circles. The larger circle has centre A and radius 20 cm. The smaller circle has centre B and radius 12 cm. The circles touch at point R. The straight line PQ is a common tangent to the circles at point P and point Q.

[Use π = 3.142]

Given that angle PAR = θ radians,

(a) show that θ = 1.32 ( to two decimal places),

(b) calculate the length, in cm, of the minor arc QR,  

(c) calculate the area, in cm², of the shaded region.

$\begin{array}{l}\text{In }△BSA\\ \cos \theta =\frac{8}{32}=\frac{1}{4}\\ \theta =1.32\text{ rad (2 d}\text{.p}\text{.)}\end{array}$

(b)
= 21.86 cm

(c)
$PQ=\sqrt{{32}^2-8^2}=30.98\text{ cm}$