Question

Let $C$ be the circle with centre at $(1,1)$ and radius = $1$. If $T$ is the circle centred at $(0,y)$, passing through 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. $\frac{1}{4}$

Answer 1

The correct option is D $\frac{1}{4}$

Consider the circle $T$ is passing through origin and having centre at $(0,y)$, hence its radius is $y$
From Rt. $△OA{O}^{\prime }$
$(y+1{)}^2=1^2+(1-y{)}^2$
$\Rightarrow y^2+1+2y=1+1+y^2-2y$
$\Rightarrow y=\frac{1}{4}$
Hence, radius $=\frac{1}{4}$