CBSE Class 10-Mathematics: Chapter –12 Areas Related to Circles Part 22
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Question 21:
In a circle of radius , an arc subtends an angle of at the center. Find:
(i) The length of the arc.
(ii) Area of the sector formed by the arc.
(iii) Area of the segment formed by the corresponding chord

Arc Subtends an Angle
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Answer:
Given,
(i) Length of arc
(ii) Area of the sector
(iii) Area of segment formed by corresponding chord
Area of segment Area of ………. (i)
In right angled triangle and ,
[Radii of the same circle]
[RHS congruency]
M is the mid-point of AB and
Therefore, in right angled triangle OMA,
Also,
Using eq. (i),
Area of segment formed by corresponding chord