Mathematics Question and Solution
Let a be the radius of the circle.
10² = 2a²+2a²cosd
50 = a²+a²cosd --- (1).
10² = (2a)²+e²
e = √(100-4a²) units.
√(100-4a²)² = 2a²-2a²cosd
100-2a² = 2a²-2a²cosd
2a²cosd = 4a²-100
cosd = (2a²-50)/a² --- (2).
Substituting (2) in (1).
50 = a²+a²(2a²-50)/a²
100 = 3a²
a² = ⅓(100)
a = ⅓(10√(3)) units.
a = 5.7735026919 units.
Again, a is the radius of the circle and also the width of the blue area.
cose = 5/a
cose = 5/⅓(10√(3))
cose = 15/(10√(3))
cose = 3/(2√(3))
cose = ½√(3) units.
e = 30°
cos30 = f/10
½√(3) = f/10
f = 5√(3) units.
f is the length of the blue area.
Therefore area blue rectangle is;
af
= ⅓(10√(3))*5√(3)
= 50 square units.
