Mathematics Question and Solution
Let the ascribed square side length be 1 units.
Calculating area red inscribed circle.
a = (1-b) units.
Where b is the radius of the red inscribed circle
sin30 = b/(1-b)
2b = 1-b
3b = 1
b = ⅓ units.
Area red inscribed circle is;
πb²
= π(⅓)²
= ⅑(π) square units.
Calculating area blue ascribed circle.
Let c be the radius of the blue inscribed circle.
cos30 = 1/d
½√(3) = 1/d
d = 2/√(3)
d = ⅓(2√(3)) units.
e = 1-d
e = ⅓(2√(3))-1
e = ⅓(2√(3)-3) units.
Therefore;
tan60 = c/(⅓(2√(3)-3))
√(3) = (3c)/(2√(3)-3)
3c = 6-3√(3))
c = (2-√(3)) units.
Again,c is the radius of the blue inscribed circle.
Area blue is;
πc²
= π(2-√(3))²
= π(4-4√(3)+3)
= (7-4√(3))π square units.
Therefore;
Area Blue : Area Red is;
(7-4√(3))π : ⅑(π)
= (63-36√(3)):1
