Question

Let the orthocentre and centroid of a triangle be $A(-3,5)$ and $B(3,3)$ 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. $2\sqrt{10}$
• D. $3\sqrt{\frac{5}{2}}$

Answer 1

The correct option is D $3\sqrt{\frac{5}{2}}$

Given: orthocentre $=A(–3,5)$, centroid $=B(3,3)$


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