Question

The arcs of the same length in two circles subtend angles of ${28}^{\circ }$ and ${35}^{\circ }$ at their centres. Then the ratio of their respective radii is

• A. $3:4$
• B. $4:3$
• C. $4:5$
• D. $5:4$

Answer 1

The correct option is D $5:4$

Let $r_1$ and $r_2$ be the radii of the given circles and let their arcs of same length subtend angles (in radians) of ${\theta }_1$ and ${\theta }_2$ at their centres.
Then $r_1{\theta }_1=r_2{\theta }_2$
$\Rightarrow r_1\times 28\times \frac{\pi }{180}=r_2\times 35\times \frac{\pi }{180}\Rightarrow \frac{r_1}{r_2}=\frac{5}{4}$