[Math] Intersection surface area of 3 circles with 3 different radius

geometry

I am trying to find the equations to calculate:

  1. The intersection surface area generated by the intersection of 3 circles (3 circles
    like a Venn Diagram).
  2. The 3 circle's radius could be be different one from others but always 0 < radius <= 1
  3. The circles centres positions are fix and they are separated by 1 unit each from other
    (the circle's centres are located in the vertexs of an equilateral triangle of side=1)

To be clearer… the intersection "of the 3 circles" area will result in a figure like an "irregular Reuleux triangle". That means a Reauleaux triangle where the internal triangle could be any (and not only an equilateral triangle) and the three radius could be different one from the others

Thanks a lot in advance

Georges L

Best Answer

Given only two similarly intersecting circles, can you find the area of their intersection?

Say $S_1, S_2, S_3$ are the circles, $T$ is the triangle and $A(s)$ is the function calculating the area of some set $s$. Then $A(\bigcap S_i) = A(T) - \sum \limits_{i <j} \Big(A(S_i \cap T) - A(S_i \cap S_j)/2 \Big)$.

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