Check whether the following statement is true or false. Justify your answer.
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.

We know that,

Arc length = $\dfrac{\theta}{360}$ × 2πr

Let L₁ and L₂ be the arc length of first circle and second circle and θ₁ and θ₂ be the central angle of the sector for the first circle and second circle respectively.

Arc length for first circle (L₁) = $\dfrac{\theta_1}{360°}$ × 2πr

Arc length for second circle (L₂) = $\dfrac{\theta_2}{360}°$ × 2π(2r)

L₂ = $\dfrac{\theta_2}{360°}$ × 4πr

According to question :

L₁ = L₂

$\dfrac{\theta$1}{360°} × 2πr = \dfrac{\theta2}{360°} × 4πr

2θ₁ = 4θ₂

θ₁ = 2θ₂

∴ Angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle.

Hence, the statement is True.