Question

The area of smaller part bounded by circle $x^2+y^2=a^2$ and the line $x=\frac{a}{\sqrt{2}}$ is $\frac{a^2}{2}(\frac{\pi }{P}-1)$. Find the value of $P$.

Answer 1

The radius of circle is $a$ , The perpendicular distance between center of circle and the given line is $\frac{a}{\sqrt{2}}$

Therefore the length of chord of circle made by line $x=\frac{a}{\sqrt{2}}$ is $\sqrt{2}a$

Therefore the area of triangle made by given line and center of circle is $\frac{a^2}{2}$

The required area will be $\frac{\pi a^2}{4}-\frac{a^2}{2}=\frac{a^2}{2}(\frac{\pi }{2}-1)$

Therefore the value of $P$ is $2$