Q19 of 68 Page 15

Fig.15.17, shows a sector of a circle, centre O, containing an angle θ°. Prove that:

(i) Perimeter of the shaded region is


(ii) Area of the shaded region is



Angle subtend at centre of circle = θ


Angle OAB = 90°


(At point of contract, tangent is perpendicular to radius)


OAB is right angle triangle




Perimeter of shaded region = AB+ BC+(CA arc)





Area of shaded region = (area of triangle AOB) – (area of sector)





More from this chapter

All 68 →
17

A sector of 56° cut out from a circle contains area 4.4cm2. Find the radius of the circle.

 18

In a circle of radius 6cm, a chord of length 10cm makes an angle of 110° at the centre of the circle. Find:

(i)the circumference of the circle,


(ii)the area of the circle,


(iii)the length of the arc AB,


(iv)the area of the sector OAB.

 20

Figure 15.18 shows a sector of a circle of radius r cm containing an angle θ°. The area of the sector is A cm2 and perimeter of the sector is 50cm.

(i)(ii)


 21

The length of the minute hand of a clock is 14cm. Find the area swept by the minute hand in 5minutes.