Question

For a $\triangle A B C$ the vertices are $A(0,3), B(0,12)$ and $C(x, 0)$. If the circumcircle of $\triangle A B C$ touches the $x$-axis, then the area (in sq. units) of the $\triangle A B C$ is

• A. 36
• B. 27
• C. 30
• D. 24

Answer 1

Answer: (B)

$OA \times OB = OC ^{2} $
$\Rightarrow 3 \times 12= x ^{2} $
$\Rightarrow x =6$
Centre $\left(C^{\prime}\right)=\left(6, \frac{15}{2}\right)$
$\angle AC ^{\prime} B =2 \angle ACB =2 \theta$
Area of $\triangle A C B=\frac{1}{2} \times 9 \times 6=27$ sq. units