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23/06/2021 11:49 am
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A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:
(i) minor segment
(ii) major sector. (Use π = 3.14)
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23/06/2021 11:53 am
Here AB be the chord which is subtending an angle 90° at the center O.
It is given that the radius (r) of the circle = 10 cm
(i) Area of minor sector = (90/360°) × πr2
= (1/4) × (22/7) × 102
Area of minor sector = 78.5 cm2
Area of ΔAOB = 1/2 × OB × OA
OB and OA are the radii of the circle = 10 cm
Area of ΔAOB = 1/2 × 10 × 10
= 50 cm2
Area of minor segment = area of minor sector – area of ΔAOB
= 78.5 – 50
= 28.5 cm2
(ii) Area of major sector = Area of circle – Area of minor sector
= (3.14 × 102) - 78.5
= 235.5 cm2