# Let C be the circle with center 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 is equal to

## Solution :

Let coordinates of the center of T be (0, k).

Distance between their center is

k + 1 = $$\sqrt{1 + (k – 1)^2}$$

where k is radius of circle T and 1 is radius of circle C, so sum of these is distance between their centers.

$$\implies$$ k + 1 =  $$\sqrt{k^2 + 2 – 2k}$$

$$\implies$$ $$k^2 + 1 + 2k$$ = $$k^2 + 2 – 2k$$

$$\implies$$ k = $$1\over 4$$

So, the radius of circle T is k i.e. $$1\over 4$$

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