question_answer

.Let C be the circle with centre at (1, 1) and radius \[=1.\] If T is the circle centred at (0, y), passing throud origin and touching the circle C externally, then the radius of T is equal to:

A) \[\frac{\sqrt{3}}{\sqrt{2}}\]

B) \[\frac{\sqrt{3}}{2}\]

C) \[\frac{1}{2}\]

D) \[\frac{1}{4}\]

Correct Answer: D

Solution :

According to the figure,

\[{{(1+y)}^{2}}={{(1-y)}^{2}}+1\,(y>0)\]

\[\Rightarrow \]   \[y=\frac{1}{4}.\]