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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.

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This is supposed to be a comment but I need to post the picture.


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).

Intersection of 3 circles

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