Question

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

A
300
B
450
C
600
D
900

Solution

## The correct option is C $$60^{0}$$Angle between circle is given by $$\cos(180-\theta )=\dfrac{r{_{1}}^{2}+r{_{2}}^{2}-d^{2}}{2r _{1}r_{2}}$$where, $$r _{1}$$ and $$r_{2}$$ are radii of two circlesd is distance between their centresand $$\theta$$ is angle $$bet^{n}$$ the circles.So, $$\cos(180-\theta )=\dfrac{4^{2}+3^{2}-37}{2\times 4\times 3}=\dfrac{-12}{2\times 4\times 3}$$$$=-\dfrac12$$$$-\cos(\theta )=-\dfrac12$$$$\cos\theta =\dfrac12$$$$\theta =60^{0}$$$$\rightarrow$$ angle $$bet^{n}$$ circles is $$60^{0}.$$Maths

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