Answer:
Option C
Explanation:
Key Idea Orthocentre, centroid and circumcentre are collinear and centroid divide orthocentre and circumcentre in 2:1 ratio.
We have orthocentre and centroid of a triangle be A ( -3,5) and ( 3,3) respectively and C circumcentre
Clearly , $AB= \sqrt{(3+3)^{2}+( 3-5)^{2} }=\sqrt{36+4}=2\sqrt{10}$
We know that, AB:BC=2:1
$\therefore$ BC= $\sqrt{10}$
Now,
AC=AB+BC=$2\sqrt{10}+\sqrt{10}=3\sqrt{10}$
Since, AC is a diameter of circle
$\therefore$ $r=\frac{AC}{2}$
$\Rightarrow$ $r=\frac{3\sqrt{10}}{2}=3\sqrt{\frac{5}{2}}$
