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If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2 r, 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

Solution:

Let us take two circles C₁ and C₂ of radii r and 2r

Consider l₁ and l₂ as the length of two arcs

Here

l₁ = \(\widehat{AB}\) of C₁ = 2πrθ₁/360

l₂ = \(\widehat{CD}\) of C₂ = 2πrθ₂/360 = 2π2rθ₂/360

We know that

l₁ = l₂

2πrθ₁/360 = 2π2rθ₂/360

θ₁ = 2θ₂

So the angle of sector of first circle is twice the angle of the sector of the other circle

Therefore, the statement is true.

✦ Try This: If an arc of a circle of radius 14 cm subtends an angle of 60° at the centre, then the length of the arc is 44/3 cm a. True, b. False

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.2 Problem 8

If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2 r, 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

Summary:

The statement “If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2 r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle” is true

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