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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__ C_{1} and C_{2} of radii r and 2r

Consider l_{1} and l_{2} as the length of two arcs

Here

l_{1} = \(\widehat{AB}\) of C_{1} = 2πrθ_{1}/360

l_{2} = \(\widehat{CD}\) of C_{2} = 2πrθ_{2}/360 = 2π2rθ_{2}/360

We know that

l_{1} = l_{2}

2πrθ_{1}/360 = 2π2rθ_{2}/360

θ_{1} = 2θ_{2}

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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