# If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double - Mathematics

MCQ
True or False

If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false? Why?

• True

• False

#### Solution

This statement is False.

Explanation:

Let two circles C1 and C2 of radius r and 2r with centres O and O’, respectively.

It is given that, the arc length hat(AB) of C1 is equal to arc length hat(CD) of C2 i.e., bar(AB) = bar(CD) = l ....(say)

Now, let θ1 be the angle subtended by arc bar(AB) of θ2 be the angle subtended by arc bar(CD) at the centre.

∴ bar(AB) = l = Q_1/360 xx 2pir   ......(i)

And hat(CD) = l = theta_2/360 xx 2pi (2r) = theta_2/360 xx 4pil  .....(ii)

From equations (i) and (ii),

theta_1/360 xx 2pir = theta_2/360 xx 4pir

⇒ theta_1 = 2theta_2

i.e., Angle of the corresponding sector of C1 is double the angle of the corresponding sector of C2.
It is true statement.

Concept: Areas of Sector and Segment of a Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.2 | Q 8 | Page 123
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