Let the orthocentre and centroid of a triangle be $A\left(-3, 5\right)$ and $B\left(3, 3\right)$ respectively. If $C$ is the circumcentre of this triangle, then the radius of the circle having line segment $AC$ as diameter, is:

• A

  $\frac{3\sqrt{5}}{2}$
• B

  $\sqrt{10}$
• C

  $2\sqrt{10}$
• Correct answer
  D

  $3\sqrt{\frac{5}{2}}$

Solution

Centroid $B$ divides the line joining Orthocentre $A$ and circumcentre $C$ in the ratio $2:1$

$AB= \sqrt{{\left(3+3\right)}^2+{\left(5-3\right)}^2}= \sqrt{6^2+2^2}= \sqrt{40}=2\sqrt{10}$

$AC=\frac{3}{2}\times 2\sqrt{10}=3\sqrt{10}$

Radius $=\frac{AC}{2}=3\sqrt{\frac{10}{4}}=3\sqrt{\frac{5}{2}}$

Hence, the correct answer is option: 'D'.