Circular Measure Structured Questions | Cambridge O Level Additional Mathematics

Question 1 of 3 · 10 marks

Circular Measure · 1 - Arc Length & Sector Area

3 parts

Additional Mathematics 4037 · Question 1Paper 2 · Calculator[10 marks]

The diagram shows a circle with centre $O$ and radius $r = 6\,\mathrm{cm}$ . Two straight line tangents $PA$ and $\ce{PB}$ are drawn from an external point $P$ to touch the circle at points $A$ and $B$ respectively. The angle between the tangents is $\angle APB = \frac{\pi}{3}\,\mathrm{radians}$ .

(a)

Show that the central angle $\angle AOB = \frac{2\pi}{3}\,\mathrm{radians}$ , and determine the exact length of the tangent segment $PA$ .

[2]

(b)

Calculate the exact perimeter of the shaded region bounded by the tangent segments $PA$ , $\ce{PB}$ and the minor arc $AB$ .

[3]

(c)

Calculate the exact area of the shaded region bounded by the tangents $PA$ , $\ce{PB}$ and the minor arc $AB$ .

[5]