Mathematics Question and Solution
Calculating R, radius of the inscribed circle.
a² = 2*3²
a = 3√(2) units.
a is the diagonal of the square.
b² = 2R²
b = √(2)R units.
c = a-b
c = (3√(2)-√(2)R) units.
It implies;
(3√(2)-√(2)R)² = R²+3²
18-12R+2R² = R²+9
R²-12R+9 = 0
Calculating R, resolving the above quadratic equation via completing the square approach.
(R-6)² = -9+(-6)²
(R-6)² = 27
R = 6±√(27)
R = 6±3√(3)
It implies;
R ≠ 6+3√(3) units.
R = 6-3√(3) units.
R = 3(2-√(3)) units.
R = 0.8038475773 units.
