AIMO 2015 Q6

Geometry Level 4

A large circle with radius \(30/ \sqrt{\pi}\) is shaded grey. Two white circles with diameter \(30/ \sqrt{\pi}\) lie inside the grey circle such that they are all tangent to one another (the two circles are internally tangent to the grey circle but are externally tangent to each other). Two more white circles of equal radii lie inside the grey circle such that both small white circles are internally tangent to the grey circle and are externally tangent to both white circles but are not tangent to each other. Find the area of the grey portion visible.

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