Calculating R, radius of the circle.
12a = 3*4
a = 1 unit.
b = ½(3+4)
b = 3.5 units.
c = b-3
c = 0.5 units.
d = 180-60
d = 120°
e² = R²-3.5²
e =√(R²-12.25) units.
f² = 1²+0.5...
Calculating R, radius of the quarter circle.
a = 3+4
a = 7 units.
b² = 2(4)²
b = 4√(2) units.
c = R-b
c = (R-4√(2)) units.
d = 180-45
d = 135°
R is;
R² = 7²+(R-4√(2))²-2*7(R-4√(2))cos135
R² =...
Let BF be a.
b² = 18²+a²
b = √(324+a²) units.
b is AB.
c = (a+14) units.
It implies;
calculating a.
(a+14) ~ √(324+a²)
√(324+a²) ~ 18
Cross Multiply.
18(a+14) = 324+a²
18a+252 = 324+a²
a²-18a+...
Let the side length of the inscribed regular triangle be a.
2b² = a²
b = √(a²/2)
b = ½√(2)a units.
c = 2b
c = √(2)a units.
c is the side length of the ascribed square.
d² = b²+c²
d² = (√(2)a)²+(½...
Let AB be 1 unit.
Let BC be a.
Therefore;
CD = (1-a) units.
It implies;
tan60 = b/(0.5a)
2b = √(3)a
b = ½√(3)a units.
b is the height of the bigger inscribed equilateral triangle....
Calculating Blue Area.
a = 8+2
a = 10 units.
a is the side length of the ascribed square and the radius of the bigger inscribed quarter circle.
b = 8 units.
b is the radius of the big insc...
Let angle AOB be a.
Let b = AD = OB = OD.
b is the radius of the quarter circle.
Calculating b.
2² = 2b²-2b²cosa
2b²cosa = 2b²-4
b²cosa = b²-2
cosa = (b²-2)/b² --- (1).
4² = b²+(2b)²-4b²cosa
16...
Let r = 1 unit.
a = (R+1) units.
b = (R-1) units.
c²+b² = a²
c²+(R-1)² = (R+1)²
c² = R²+2R+1-(R²-2R+1)
c = √(4R)
c = 2√(R) units.
d = R+2-R
d = 2 units.
e = R+R
e = 2R units.
Calculating R....
Notice.
The ascribed quadrilateral is regular (square).
Let a be it's side length.
½*ab = 3
ab = 6
b = (6/a) units.
b is the base of the red area.
½*ac = 4
ac = 8
c = (8/a) units....
tan60 = a/(0.5*8)
a = 4tan60
a = 4√(3) cm.
a is the diameter of the circle.
b = ½(a)
b = 2√(3) cm.
b is the radius of the circle.
c = ¼(8)
c = 2 cm.
c is the radius of the two equal half circles....
