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Q.

Let A(1,2) be the centre and 3 be the radius of a circle S. Let B(-1,-1) be the centre and r be the radius of another circle S¹. If $\frac{π}{3}$ is the angle between the circles S and S¹, then the number of possible values of r is

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a

2

b

1

c

3

d

4

answer is B.

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Detailed Solution

Angle between two circles is

$\cos θ = \frac{d^{2} - {r_{1}}^{2} - {r_{2}}^{2}}{2 r_{1} r_{2}}$

$\cos \frac{π}{3} = \frac{{(\sqrt{13})}^{2} - {(3)}^{2} - r^{2}}{2 (3) r}$

$\frac{1}{2} = \frac{{(\sqrt{13})}^{2} - {(3)}^{2} - r^{2}}{2 (3) r}$

two r values are possible

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