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 =…

Given circle $x^2+y^2=1$

General coordinate on a given circle is $\left(\cos \theta , \sin \theta \right).$

Given, $h=\frac{\cos \theta +3}{2}\Rightarrow \cos \theta =2\left(h-\frac{3}{2}\right) ...\left(i\right)$

$k=\frac{\sin \theta +2}{2}\Rightarrow \sin \theta =2\left(k-1\right) ...\left(ii\right)$

Square $\left(i\right) \& \left(ii\right)$then add we get, 

${\left(h-\frac{3}{2}\right)}^2+{\left(k-1\right)}^2={\left(\frac{1}{2}\right)}^2$

$\Rightarrow r=\frac{1}{2}$