If AB is a chord of circle with centre O. And AOB = 90. If diameter is 10 cm then find AB.
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Class 10>>Maths>>Areas Related to Circles>>Area of Sector and Length of an Arc>>A chord of a circle of radius 10 cm subt
Question
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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Solution
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In the mentioned circle,
O is the centre and AO =BO = Radius = 10 cm
AB is a chord which subtents 90o at centre O, i.e., ∠AOB=90o
(i)
Area of minor segment APB (Shaded region) = Area of Sector AOB - Area of △AOB
=(4π×10×10)−(0.5×10×10)
=78.5−50
=28.5cm2
(ii)
Area of Major sector = Area of circle - Area of Sector AOB
= (π×10×10)−(4π×10×10)
=314−78.5
=235.5cm2
In the mentioned circle,
O is the centre and AO =BO = Radius = 10 cm
AB is a chord which subtents 90o at centre O, i.e., ∠AOB=90o
(i)
Area of minor segment APB (Shaded region) = Area of Sector AOB - Area of △AOB
=(4π×10×10)−(0.5×10×10)
=78.5−50
=28.5cm2
(ii)
Area of Major sector = Area of circle - Area of Sector AOB
= (π×10×10)−(4π×10×10)
=314−78.5
=235.5cm2
.