Question

ABC is a right angled triangle wit $\angle B=90{}^{\circ },$ $a=6cm$ . If the radius of the circumcircle is 5 cm, then the area of $\Delta ABC$ is

• A. $25c{m}^2$
• B. $30c{m}^2$
• C. $36c{m}^2$
• D. $24c{m}^2$
• E. $48c{m}^2$

Answer 1

Answer: (D)

Let D be the centre of circumcircle.

$\therefore$ $BD=5cm$
In $\Delta ABC,$ $A{C}^2=A{B}^2+B{C}^2$
$\Rightarrow$ $100=A{B}^2+B{C}^2$
$\Rightarrow$ $A{B}^2=64$
$\Rightarrow$ $AB=8$
$\therefore$ Area of $\Delta ABC=\frac{1}{2}\times AB\times BC$
$=\frac{1}{2}\times 8\times 6=24c{m}^2$