Question

The circumradius of the triangle whose sides are $13$, $12$, and $5$ is

• A. $15$
• B. $13/2$
• C. $15/2$
• D. $6$

Answer 1

The correct option is B

$13/2$

Explanation for the correct option :

Finding the circumcenter and radius of the triangle:

The sides of a triangle are of length $13,12$ and $5$.

Let $a=13,b=12,c=5$.

Then $a^2=b^2+c^2$.

Hence the triangle is a right-angled triangle with hypotenuse length $13$.

So, the circumcenter lies at the midpoint of the hypotenuse and its radius is half of the hypotenuse length.

$\therefore r=\frac{13}{2}$.

Therefore, Option (B) is correct.