Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). Then tangent at the point to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is

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$\sqrt{2}$

$2 \sqrt{2}$

answer is D.

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Detailed Solution

$F r o m d i a g r a m C_{1} A C_{2} D i s a s q u a r e t h e n C_{1} C_{2} = \sqrt{2} r a n d C_{1} D = \frac{\sqrt{2} r}{2} = \frac{r}{\sqrt{2}} F r o m ∆ B C_{2} D \Rightarrow 1 + \frac{r^{2}}{2} = r^{2} \Rightarrow r^{2} = 2 \Rightarrow r = \sqrt{2} N o w C_{1} C_{2} = 2$

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