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Question

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding major sector.

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Solution

Radius r=10cm

angle=90

area of sector A=90360πr2

A=3.14×10×104

A=25×3.14

A=78.5sq.cm

Let the angle subtended and radius form an arc AOB, then

area of AOB=r×r×sin902

AOB=10×10×12

ar. of AOB =50sq.cm

area of minor segment =78.550

=28.5aq.cm

Then the area of circle =πr2

=3.14×10×10

=314Sq.cm

area of major segment =area of the circle -area of the minor segment

=31428.5

=285.5sq.cm

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