Question

Let the orthocenter an 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. $\sqrt{10}$
• B. $2 \sqrt{10}$
• C. $3 \sqrt{\frac{5}{2}}$
• D. $\frac{3\sqrt{5}}{2}$

Answer 1

Answer: (C)

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

Answer 2

$A(-3,5)$
$B(3,3)$

So, $A B=2 \sqrt{10}$
Now, as, $A C=\frac{3}{2} A B$
So, radius $=\frac{3}{4} A B=\frac{3}{2} \sqrt{10}=3 \sqrt{\frac{5}{2}}$