Quarter circle arc 
These are congruent sectors (aka quarter circle) with the arc of the lower circle bisects the radius of the upper circle and the radii are parallel. My question is: Is the overlapped part a quarter circle?
My opinion: The arc of the overlapped segment belongs to the circle with point$A$ so it is not a sector

If the intersection of the two quarter circles was a circular sector, let alone a quarter circle, the angle between the straight lines and the arc would be $90^\circ$. It is rather obvious from the diagram that that angle is less than $90^\circ$. So the intersection is not a quarter circle.
