Calculating The Required Angle.
Let it be x.
a = ½(12)+b
a = (6+b) cm.
b is the radius of the inscribed sector.
Calculating b.
c² = 6²+12²
c² = 36+144
c = √(180)
c = 6√(5) cm.
I...
Calculating Shaded Fraction.
Let the radius of the inscribed circle be 1 unit.
Therefore, the radius of the inscribed half circle is 2 units.
a² = 2²+(2+2)²
a² = 20
a = 2√(5) units.
a i...
Calculating Inscribed Blue Rectangle Area.
a = 15+5
a = 20 units.
Let b be the length of the blue inscribed rectangle.
b² = 2(20)²-2(20)²cos(90-x)
b² = 800-800(cos90cosx+sin90sinx)
b² =...
Calculating x.
Let a be the side length of the square.
b² = 2a²
b = √(2)a units.
c = ½(b)
c = ½√(2)a units.
a ~ 1
0.5 ~ d
Cross Multiply.
d = 1/(2a) units.
Calculating a.
c+d...
Calculating x.
10² = 18²+x²-2*18xcosy
36xcosy = 224+x²
cosy = (224+x²)/(36x) --- (1).
10² = 6²+x²-2*6xcosy
12xcosy = x²-64
cosy = (x²-64)/(12x) --- (2).
Equating (1) and (2).
(224+x...
Calculating Ratio Purple Area and Orange Area.
Let 2 be the radius of the inscribed orange area.
It implies;
Area orange inscribed circle is;
π(2)²
= 4π square units.
tan30 = 2/a
a = 2√(3) unit...
Calculating Area Inscribed yellow Circle.
Let x be the area of the ascribed circle.
a*12 = 5*9
a = (45/12)
a = ¼(15) units.
a = 3.75 units.
b = ½(a+12)
b = ½(15.75)
b = 7.875 units....
Calculating Area Blue.
a = ½(4)
a = 2 units.
a is the radius of the inscribed half circle.
b = (2+x) units.
x is the radius of the inscribed circle.
c = (4-x) units.
It implies;
d²+x² = (4-x)²...
Calculating R, radius of the circle.
R² = 8²+5²-2*8*5cosx
R² = 89-80cosx --- (1).
a = (90-x)°
R² = 5²+12²-2*5*12cos(90-x)
R² = 169-120cos(90-x)
R² = 169-120(cos90cosx-sin90sinx)
R² = 1...
Calculating angle x.
Let CD = 1 unit.
(1/sin30) = (a/sin(180-20-20-30))
a = 1.87938524157 units.
a is BC.
cos20 = (½(BC))/b
cos20 = (0.5*1.87938524157)/b
b = 0.93969262079/cos20
b = 1 unit.
b is...
