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A line segment AB of length $λ$ moves such that the points A and B remain on the periphery of a circle of radius $λ$ . Then the locus of the point, that divides the line segment AB in the ratio 2 : 3, is a circle of radius

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$\frac{3}{5} λ$

$\frac{2}{3} λ$

$\frac{\sqrt{19}}{5} λ$

$\frac{\sqrt{19}}{7} λ$

answer is D.

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Detailed Solution

$AC = \frac{λ}{2}, AM = \frac{2 λ}{5}, CM = \frac{λ}{10}, {OM}^{2} = {CM}^{2} + {OC}^{2} \Rightarrow x^{2} + y^{2} = \frac{19 λ^{2}}{25}$

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