plotting – Filling between three curves

I have been trying to fill the area between the three curves on the graph below (area between the points a, b, and c), but have had no successful result so far. I kept a simple filling command to ask how I can manipulate it in a way that I can fill the area between these points. Any help would be greatly appreciated. Here is my command:

Plot({31.25/x, 11.1803 - x, Sqrt(100 - x^2)/2, Sqrt(100 - 4 x^2)}, {x, 0, 12}, PlotRange -> {0, 12}, Filling -> {2 -> {{3}, {None, Gray}}}, Epilog -> {Text(Style(TraditionalForm(a), Black, FontSize -> 12), {2.23607, 8.94}), Text(Style(TraditionalForm(b), Black, FontSize -> 12), {4.45, 4.45}),Text(Style(TraditionalForm(c), Black, FontSize -> 12), {8.94, 2.23607})})