Find the area of the smaller part of the circle x² + y² = a² cut off by the line

Question

Find the area of the smaller part of the circle x 2 + y 2 = a 2 cut off by the line

Philoid · Accepted Answer

It is given that the area of the smaller part of the circle cut off by the line

From the figure we can see that the area is ABCDA and it is shown by shaded region.

Now, we can observed that the area ABCD is symmetrical about x-axis.

Area ABCD = 2 × Area ABC

Area of ABC =

Therefore, required area is =

Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line