Question

Find the area of the circle if the area of an isosceles right triangle inscribed in it is 18 $c{m}^2$

• A. 16$\pi$
• B. 21$\pi$
• C. 18$\pi$
• D. 24$\pi$

Answer 1

Answer: (C)

18$\pi$

Let the sides of right angles isosceles triangle be $a,a,\sqrt{2}a$

The area of triangle is $\frac{1}{2}{a}^2=18$

$\Rightarrow a=6$

The center of circumcircle of right angled isosceles triangle is center of hypotenuse

So the radius of circle is $\frac{6}{\sqrt{2}}=3\sqrt{2}$

Therefore area of circle is $\pi \times 3\sqrt{2}\times 3\sqrt{2}=18\pi$

So the correct option is $C$