There are some issues with Problem D and E. Gonitzoggo team should be more careful about the problems of Calibration Round. It’s rated.
In Problem D,
The area [GDEF]=4. But a+\sqrt{b}=4 has infinitely many solutions. So, there is no absolute answer to this question.
In Problem E,
AC=2r, so, AC is the diameter and \angle AOC=180\degree. And given, \angle AOC=2\angle BOD. So, \angle BOD=90\degree.
Clearly, OB=OD=r.
Using Pythagoras, BD=\sqrt{r^2+r^2}
And given, BD=r\sqrt{3},
That leads to, r\sqrt{2}=r\sqrt{3} \Rightarrow \sqrt{2}=\sqrt{3}
That’s a mathematical contradiction.