Mathematics Question and Solution
Let a be the radius of the inscribed green circle.
tan30 = a/b
b = √(3)a cm.
c = ½(3√(3)-π) cm²
d = 60π*a²/360
d = ⅙(πa²) cm²
Therefore;
0.5*a*√(3)a = ½(3√(3)-π)+⅙(πa²)
½√(3)a² = ½(3√(3))-½(π)+⅙(πa²)
3√(3)a² = 9√(3)-3π+πa²
3√(3)a²-πa² = 9√(3)-3π
a²(3√(3)-π) = (9√(3)-3π)
a² = (9√(3)-3π)/(3√(3)-π)
It implies;
a = 1.7320508076 cm.
a = √(3) cm.
Again, a is the radius of the inscribed green circle.
Area inscribed green circle is;
πa²
= π√(3)²
= 3π cm²
