Question

lf radii of two circles are $4$ and $3$ and distance between centres is $\sqrt{37}$ , then angle between the circles is

• A. ${30}^0$
• B. ${45}^0$
• C. ${60}^0$
• D. ${90}^0$

Answer 1

The correct option is C ${60}^0$

Angle between circle is given by $\cos (180-\theta )=\frac{r{{}_1}^2+r{{}_2}^2-d^2}{2r_1{r}_2}$
where, $r_1$ and $r_2$ are radii of two circles
d is distance between their centres
and $\theta$ is angle $be{t}^n$ the circles.
So, $\cos (180-\theta )=\frac{4^2+3^2-37}{2\times 4\times 3}=\frac{-12}{2\times 4\times 3}$
$=-\frac{1}{2}$
$-\cos \left(\theta \right)=-\frac{1}{2}$
$\cos \theta =\frac{1}{2}$
$\theta ={60}^0$
$\to$ angle $be{t}^n$ circles is ${60}^0.$