Q24 of 37 Page 13

A chord of a circle of radius 12cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle [Use π=3.14,√3=1.73]


Given: Radius of the circle = OA = OB = 12cm


and θ = 120°


To find: Area of the corresponding segment of the circle


i.e. Area of segment APB = Area of sector OAPB – Area of ΔAOB


So, firstly we find the Area of sector OAPB





= 150.72cm2


Now, we have to find the area of ΔAOB


We draw OM ⊥ AB


∴∠OMB = ∠OMA = 90°


In ΔOMA and ΔOMB


∠OMA = ∠OMB [both 90°]


OA = OB [both radius]


OM = OM [common]


∴ OMA ≅ ΔOMB [by RHS congruency]


⇒ ∠AOM = ∠BOM [CPCT]




∴In right triangle OMA, we have




⇒ AM = 6√3 cm


⇒ 2AM =12√3 cm


⇒ AB =12√3 cm


and




⇒ OM = 6cm




= 36√3


= 36 × 1.73


= 62.28 cm2


Area of segment APB = Area of sector OAPB – Area of ΔAOB


= (150.72 – 62.28)


= 88.44 cm2


More from this chapter

All 37 →
22

A chord of a circle of radius 10cm subtends a right angle at the centre. Use π=3.14 and find:

(i) area of the minor sector


(ii)area of the major sector

 23

In a circle of radius 21 cm, and arc subtends an angle of 60° at the centre. Find

(i) length of arc


(ii) area of the sector formed by the arc


(iii) area of the segment formed by the corresponding chord of the arc.

 25

A brooch is made with silver wire in the form of a circle with diameter 35mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure. Find:

(i) the total length of the silver wire required.


(ii) the area of each sector of the brooch


 26

A horse is tied to a pole at one corner of a square grass field of side 15 m using 10 m long rope. Find

(i) the area of that part of the field in which the horse can graze.


(ii) the decrease in the grazing area if the rope was 5 m long instead of 10m. [Use π=3.14]