Q (6) If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Answers (1)

Solution

Given:-     
            \theta_1 = 60\degree\\ \theta_2 = 75\degree\\        and      l_1 = l_2 

We need to find  the ratio of their radii     \frac{r_1}{r_2} = ?

We know that arc length  l = r \theta
So, 
                         l_1 = r_1 \theta_1\\l_2 = r_2\theta_2         
Now, 
               \frac{l_1}{l_2}=\frac{ r_1 \theta_1}{ r_2\theta_2}                           ( l_1 = l_2)
So,
         \frac{ r_1 }{ r_2}= \frac{\theta_2}{\theta_1} = \frac {75}{60} = \frac{5}{4}         is the ratio of their radii 

 

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