Question

If the locus of the mid-point of the line segment from the point $(3,2)$ to a point on the circle , $x^2+y^2=1$ is a circle of the radius $r$ then $r$ is equal to :

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $\frac{1}{3}$

Answer 1

The correct option is B $\frac{1}{2}$


$\therefore P\equiv (2h-3,2k-2)\to$ on circle
$\therefore {(h-\frac{3}{2})}^2+(k-1{)}^2=\frac{1}{4}$
$\Rightarrow r=\frac{1}{2}$