Percentage area of circles overlapping a triangle
I have an interesting problem regarding the area coverage of a triangle, in relation to the diameter of three equal circles centred at each of its three vertices (please see attached image).
Is it possible to formulate a function that will exact the required circle diameter for a given percentage-coverage of the triangular area? For example, what would be the correct circle diameter for an 89% coverage of the triangular area (i.e. 11% of the triangular area is not obscured).
As the circles will need to overlap in order to accommodate the complete 0% - 100% range, is it possible to create a unified formula or will the overlapped and non-overlapped percentages need to be addressed separately?
Any help or insight would be most appreciated.
Best regards, Gemma.