Circles Part 1

Given, circle x2+y2=1
Let (h,k) be the mid-point of line segment from point (3,2) to a point on circle. Let point on circle be (a,b). Then,
‌h=‌

a+3

2

⇒a=2h−3
‌k=‌

b+2

2

⇒b=2k−2
∵(a,b) is point on circle, then
(a)2+(b)2‌‌=1
⇒‌‌(2h−3)2+(2k−2)2‌‌=1
⇒‌‌(h−‌

3

2

)2+(k−1)2=‌

1

4

‌‌=(‌

1

2

)2
which is an equation of circle with radius 1∕2.
∴ Radius =1∕2.