# If the Arcs of the Same Length in Two Circles Subtend Angles 65° and 110° at the Centre, than the Ratio of the Radii of the Circles is - Mathematics

MCQ

If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is

• 22 : 13

• 11 : 13

• 22 : 15

• 21 : 13

#### Solution

22:13
Let the angles subtended at the centres by the arcs and radii of the first and second circles be $\theta_1\text{ and } r_1\text{ and }\theta_2\text{ and }r_2 ,$ respectively.
We have:
$\theta_1 = 65^\circ = \left( 65 \times \frac{\pi}{180} \right)\text{ radian }$

$\theta_2 = 65^\circ = \left( 110 \times \frac{\pi}{180} \right)\text{ radian }$
$\theta_1 = \frac{l}{r_1}$
$\Rightarrow r_1 = \frac{l}{\left( 65 \times \frac{\pi}{180} \right)}$
$\theta_2 = \frac{l}{r_2}$
$\Rightarrow r_2 = \frac{l}{\left( 110 \times \frac{\pi}{180} \right)}$
$\Rightarrow \frac{r_1}{r_2} = \frac{\frac{l}{\left( 65 \times \frac{\pi}{180} \right)}}{\frac{l}{\left( 110 \times \frac{\pi}{180} \right)}} = \frac{110}{65} = \frac{22}{13}$
$\Rightarrow r_1 : r_2 = 22: 13$
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 4 Measurement of Angles
Exercise 4.1 | Q 5 | Page 17