Question

In given figure triangle ABC circumscribes the circle with center O and radius $2cm$.

Area of $\Delta ABC$ is $16c{m}^2$. find AB

• A. $5cm$
• B. $6cm$
• C. $7cm$
• D. $8cm$

Answer 1

The correct option is A $5cm$

Area of $\Delta ABC=Areaof(\Delta AOB+\Delta BOC+\Delta AOC)$

$=\frac{1}{2}\times OR\times BC+\frac{1}{2}\times OP\times AB+\frac{1}{2}\times OQ\times AC$

Let $AP=AQ=x$

$\therefore AB=AP+PB=AP+RB=x+2$

$\therefore AC=x+3$

$\therefore A\left(\Delta ABC\right)=\frac{1}{2}\times 2\times 5+\frac{1}{2}\times 2\times (x+2)+\frac{1}{2}\times 2\times (x+3)$

$\Rightarrow 2x+10=16\Rightarrow x=3$

$\therefore AB=5cm$