Viral question on YouTube. But let me start by saying the guy got it wrong. We don't do such things at the age of 11, we do this question about Year 11 (aged 14/15, 16 for some).
Tried this
f1 = 10 - Sqrt[10^2 - x^2];
f2 = 5 - Sqrt[5^2 - (x - 5)^2];
f3 = 5 + Sqrt[5^2 - (x - 5)^2];
And
r00 = Graphics[{EdgeForm[Thick], Transparent, Rectangle[{0, 0}, {10, 10}]}]
r0 = Plot[{f1, f2, f3}, {x, 0, 10}, Frame -> True, AspectRatio -> 1, PlotRange -> {{-0.5, 10.5}, {-0.5, 10.5}}]
r1 = Plot[{f1, f2, f3}, {x, 6.25 - 1.25 Sqrt[7], 6.25 + 1.25 Sqrt[7]}, Filling -> {1 -> {2}}, Frame -> True, AspectRatio -> 1, PlotRange -> {{-0.5, 10.5}, {-0.5, 10.5}}]
r2 = Plot[{f1, f2, f3}, {x, 6.25 + 1.25 Sqrt[7], 10}, Filling -> {3 -> {2}}, Frame -> True, AspectRatio -> 1, PlotRange -> {{-0.5, 10.5}, {-0.5, 10.5}}]
Show[{r00, r0, r1, r2}]
Surely there is a simpler way to do this?