Question

The circum-radius of the triangle whose sides are $13,12$ and $5$ is

• A. $15$
• B. $\frac{13}{2}$
• C. $\frac{15}{2}$
• D. $6$

Answer 1

Answer: (B)

Let sides be $a=13,b=12,c=5$.
Now, $a^2=b^2+c^2$
$\Rightarrow (13{)}^2=(12{)}^2+5^2$
$\Rightarrow 169=169$
$\Rightarrow \angle A=90^{\circ }$
We know, $R=\frac{a}{2\sin A}$
$=\frac{13}{2\cdot \sin 90^{\circ }}=\frac{13}{2}$