Mathematics Question and Solution
Let angle AOB be a.
Let b = AD = OB = OD.
b is the radius of the quarter circle.
Calculating b.
2² = 2b²-2b²cosa
2b²cosa = 2b²-4
b²cosa = b²-2
cosa = (b²-2)/b² --- (1).
4² = b²+(2b)²-4b²cosa
16 = 5b²-4b²cosa
4b²cosa = 5b²-16
cosa = (5b²-16)/(4b²) --- (2).
Equating (1) and (2).
(b²-2)/b² = (5b²-16)/(4b²)
4(b²-2) = 5b²-16
4b²-8 = 5b²-16
b² = 8
b = √(8)
b = 2√(2) units.
Again, b is the radius of the quarter circle.
