If the locus of the mid-point of the line segment from the point...

Given circle ${x}^{2} + {y}^{2} = 1$

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

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

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

Square \left(i\right)\text{ and }\left(ii\right)then add we get,

${\left(h - \dfrac{3}{2}\right)}$^{2} + {\left(k - 1\right)}^{2} = {\left(\dfrac{1}{2}\right)}^{2}$</p><p>$⇒ r = $\dfrac{1}{2}</p><p><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/74f0025b-531e-406d-9ac7-2584249000e1-image.png" style="width: 344px; height: 180px;" /></p>$