The purpose of this essay is to explore the area formed by the intersection of overlapping circles and how it is affected by the distance between their centers. Ángel M. Carreras Jusino . by. 1 and 2 Figure 1 shows two circles (with centers C1 and C2 and radii r_1 and r_2) that intercept each other in points A and B. Similarly to the article about intersection points of two circles we're now interested in the area that is formed by the intersection of two overlapping circles. How many smaller circles fits witin a larger circle? The area of interest is encompassed by arcs ADB and AEB. The triangular lattice form, with circle radii equal to their separation is called a seven overlapping circles grid. It contains 6 circles intersecting at a point, with a 7th circle centered on that intersection. If three symmetrically placed equal circles intersect in a single point, as illustrated above, the total area of the three lens-shaped regions formed by the pairwise intersection of circles is given by If radii r 1, r 2 and distance d between the centers are given - then the angles α 1 and α 2 can be calculated as . We could formulate cases to step through the same as in the other article, but I will do it a little shorter this time. The area contained in regions with overlapping circles is calculated and compared to the area of the bounding circle (the dotted circle) that has radius 2. Consider Figs. Thanks to Eric Eberly for providing this information. Area of Overlapping Circles. Calculate the area of the circular sector, from which subtract the area of the triangles whose base is the circles' chord defined by the intersection points; finally sum the results. In order for half the area of two unit disks () to overlap, set in the above equation (17) and solve numerically, yielding (OEIS A133741). How many circles fits within a rectangle? Calculate the intersection area of two circles July 14th, 2016. The area of intersecting circles can be calculated as. Contributed by: Simon Tyler (December 2011) In this Demonstration, the gray circle is a unit circle centered at the origin, and unit circles are placed evenly on its circumference.