# Area of the common region of three circles.

Find the area of the region that is common to the circles $$r = 1$$, $$r = 2 \cos θ$$, and $$r = 2 \sin θ$$.

I tried many ways to get the common region, but it seems impossible to eliminate to that point, but I am not sure about that either.I just need a cue.

It is a problem from Howard Anton Calculus 9th edition (page 764, Q.25). I couldn't get the Solution Manual free.

Hint: The area you want is the triangular region $$ABC$$ bounded by 3 circular arcs. You can decompose it into two circular segments ($$AC$$, $$AB$$ in red) and one circular sector ($$ABC$$ in orange).