Question

If BC passes through the centre of the circle, then the area of the shaded region in the given figure is

• A. $\frac{a^2}{2}(3-\pi )$
• B. $a^2(\frac{\pi }{2}-1)$
• C. $2a^2(\pi -1)$
• D. $\frac{a^2}{2}(\frac{\pi }{2}-1)$

Answer 1

The correct option is D $\frac{a^2}{2}(\frac{\pi }{2}-1)$

Area of shaded region $=$ Area of semicircle CABC $-$ Area of triangle ABC

$=\pi \frac{a^2}{4}-\frac{a^2}{2}$ ..... (Since $ABC$ is a right angled triangle,with base and height both $=a$ )

(Radius of circle is $\frac{a}{\sqrt{2}}$)

$=\frac{a^2}{2}(\frac{\pi }{2}-1)$