area of figure in sector of intersecting circles I need to find an area of blue part of figure APBC. I draw line segments between B and C, between C and A, and got equilateral triangle. I'm stuck here. Please help. Thanks.

|AB| = a, P is midpoint of segment AB
As achille hui says in the coments, $$(1-r)^2  = |AF|^2 =  \frac{1}{2^2} + |PF|^2 =  \frac{1}{2^2} + |DF|^2 - \frac{1}{4^2}  = \frac{1}{2^2} + \left(r + \frac14\right)^2 - \frac{1}{4^2}.$$ Solve for $r$ and you get $r=\dfrac{3}{10}.$

Since area of intersection between the two larger circles is $\dfrac{2\pi}{3}-\dfrac{\sqrt{3}}{2}$ (see here), shaded area is

\begin{align}
&amp;\dfrac{1}{2}\left(\dfrac{2\pi}{3}-\dfrac{\sqrt{3}}{2}\right)-\pi\left(\dfrac{1}{4}\right)^2-\pi\left(\dfrac{3}{10}\right)^2\\
\\
&amp; = \dfrac{217 \pi }{1200}-\dfrac{\sqrt{3}}{4}\\
\end{align}
If you know the radius of the circles it would be really simple.

You could just find the area of the intersection and subtract the area of the circle with diameter AP and the are of the circle between.