Mathematics Question and Solution
Calculating area blue.
a²+1² = 2²
a = √(3) units.
a is the diameter of the inscribed white circle.
b = ½(a)
b = ½√(3) units.
b is the radius of the inscribed white circle.
cos30 = 1/c
½√(3) = 1/c
√(3)c = 2
c = ⅔√(3) units.
c is the radius of the bigger ascribed circle.
Or
d = 180-30-30
d = 120°
Therefore;
2² = 2c²-2c²cos120
4 = 3c²
c² = 4/3
c = 2/√(3)
c = ⅔√(3) units.
Area Blue is;
π(c)²-π(a)²
= π(⅔√(3))²-π(½√(3))²
= π((4/3)-(3/4))
= 7π/12 square units.
