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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

  • $\begingroup$ Your thought is correct $\endgroup$ Oct 6, 2020 at 7:35
  • $\begingroup$ Curvature of a circle depends on its radius. $\endgroup$
    – cosmo5
    Oct 6, 2020 at 8:10

1 Answer 1


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.


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