Let a be 1 unit.
(1/sin48) = (b/sin24)
b = 0.54731813925 units.
(1/sin48) = (c/sin108)
c = 1.27977277603 units.
DC = 1.27977277603+0.54731813925+1
DC = 2.82709091528 units.
Therefore, the requi...
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Let the small inscribed circle's radius be x.
x = 6 cm.
Let the big inscribed circle's radius be y.
y = 8 cm.
Let the ascribed semi circle's radius be z.
= 18 cm.
a² = 10²-8²
a = 6 cm.
b² = 12²...
Let r be the radius of the circle.
3x+3 = 2r --- (1).
r² = (r-1)²+(r-2x)²
r² = r²-2r+1+r²-4xr+4x²
4xr+2r = r²+4x²+1 --- (2).
From (1).
3x+3 = 2r
x = ⅓(2r-3) --- (3).
Calculating r.
Therefore,...
Notice;
Hexagon Area = 24√(3) square units.
Calculating hexagon side length.
Let it be a.
(6a²)/(4tan30) = 24√(3)
½(3√(3))a² = 24√(3)
3a² = 48
a = 4 units.
Equation of the curve is;
y = ½(x²)...
Let b = 1 unit.
(1/sin72) = (a/sin48)
a = 0.78138871113 units.
BD = 1-0.78138871113
BD = 0.21861128887 units.
(AD)² = 1+0.21861128887²-2*0.21861128887cos60
AD = 0.91059299731 units.
Calculating...
a = atan(3/2)°
b = atan(2/3)°
b = Angle BEG.
tan(atan(2/3)) = c/2
⅔ = c/2
c = (4/3) cm.
c = BG.
OG = 2-(4/3)
OG = ⅔ cm.
Notice;
Radius of the circle is 2 cm.
Angle OGH = 180-atan(3/2) = 123.69...
Let DE be 1 unit.
AC = 4 units.
Area ABC is;
8sin60
= 4√(3) square units.
a² = 1+2²-4cos45
a = 1.47362575821 units.
(1.47362575821/sin45) = (1/sinb)
b = 28.6750500631°
c = 60-b
c = 31.32494993...
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a² = √(8)
a = 2√(2) units.
a is the diameter of the orange half circle.
b = ½(a)
b = √(2) units.
b is the radius of the orange half circle.
Calculating c, radius of the inscribed purple circle.
2...
