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Q.

Let C be the circle with centre at (1,1) and radius = 1. If T is the circle centered at (0,y), passing through origin and touching the circle C externally, then the radius of $T =$

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a

$\frac{1}{2}$

b

$\frac{1}{4}$

c

$\frac{\sqrt{3}}{\sqrt{2}}$

d

$\frac{\sqrt{3}}{2}$

answer is B.

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Detailed Solution

detailed_solution_thumbnail

Let r be the radius of the circle with centre $(0, y)$ . Circle passing through origin

$∴ r = y$

Given two circles touch each other externally.

$∴ c_{1} c_{2} = r_{1} + r_{2} \Rightarrow r + 1 = \sqrt{1^{2} + (y - 1)^{2}}$

$\Rightarrow (r + 1)^{2} = 1 + (r - 1)^{2} \Rightarrow r = \frac{1}{4}$

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Let C be the circle with centre at (1,1) and radius = 1. If T is the circle centered at (0,y), passing through origin and touching the circle C externally, then the radius of T=