Question

In figure, if triangle $ABC$ is an isosceles triangle of perimeter $20$, calculate the approximate area of the circle with center O.

• A. $26.83$
• B. $33.65$
• C. $44.17$
• D. $57.33$
• E. $229.34$

Answer 1

The correct option is D $57.33$

Triangle $ABC$ is isosceles

$\therefore BC=AC=\frac{(20-4)}{2}=8$ (given perimeter $20$)
In triangle $ACD$ , angle $ACD$ is $90$ degrees , because angle made by diameter at any point on circle is ${90}^o$.
Therefore we get

${AD}^2=A{C}^2+{CD}^2$

$\Rightarrow {AD}^2=64+9=73$
$\Rightarrow AD=2r=\sqrt{7}3$

$\Rightarrow r=\frac{\sqrt{73}}{2}$ ($r$ is radius )
Area of circle is $\frac{22}{7}\times {\left(\frac{\sqrt{73}}{2}\right)}^2=\frac{22\times 73}{7\times 4}=57.33$