CBSE Class 10-Mathematics: Chapter – 12 Areas Related to Circles Part 22 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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

Answer:

Given,

(i) Length of arc

(ii) Area of the sector

(iii) Area of segment formed by corresponding chord

Area of segment Area of

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