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

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