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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
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B
450
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C
600
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D
900
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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 circles
d is distance between their centres
and $$\theta$$ 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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