Notice.
r is the radius of the inscribed yellow half circle.
r = ½(10)
r = 5 units.
Calculating R, radius of the ascribed circle.
Calculating R.
a = x+10+5
a = (x+15) units.
b = ½(a)
b = ½(x+1...
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Solution and answer by Mehmet Kara.
Thank you nicely.
Let AC = BD = DE = a.
Calculating a.
14² = a²+(10+a)²-2a(10+a)cosb
96 = 2a²+20a-(20a+2a²)cosb --- (1).
14² = a²+10²+2a*10cosb
96 = a²+20acosb
cosb = (96-a²)/(20a) --- (2).
Substituting (2) in (1...
Calculating Purple Area.
tanb = 2/1
b = atan(2)°
tanc = ½
c = atan(½)°
d = 180-b
d = (180-atan(2))°
e = 180-d-c
e = 180-(180-atan(2))-atan(½)
e = (atan(2)-atan(½))°
It implies;
(1/sin(atan(2)-...
Let 1 unit be the side length of the green square.
Therefore;
EN = ½ units.
a = (1+2x) units.
a is the diameter of the bigger circle.
b = ½(a)
b = ½(1+2x) units.
b is the radius of the...
R ~ (a+b)
r ~ a
Cross Multiply.
aR = r(a+b)
R/r = (a+b)/a
R/r = 1+(b/a)
And R/r = phi (golden ratio)
Let phi be x.
x-1 = b/a
a/b = 1/(x-1)
Where x (phi) is;
x = ½(1+√(5))...
Calculating Area A Divided By Area B (A/B).
Let a be the two equal lengths.
b = (3-a) units.
c² = 4²+3²
c = 5 units.
Therefore;
Calculating a.
5 ~ (3-a)
4 ~ a
Cross Multiply.
5x = 12-4a
9a = 1...
Let DC = 1 unit.
a = 180-36+30
a = 114°
a is angle BDC.
(1/sin36) = (b/sin114)
b = 1.55421636402 units.
b is BC.
c = 180-60-54
c = 180-114
c = 66°
c is angle BAC.
Therefore;
(1.55421636402/sin6...
Calculating R.
3R+4R+5R = 3*4
12R = 12
R = 1 units.
Calculating r.
tana = 3/4
a = atan(3/4)°
b = ½(a)
b = ½(atan(3/4))°
tan(½(atan(3/4))) = r/c
c = 3r units.
d = 4-1-3r
d = (3-3r) units.
e...
Let the height and base of the brown area be x and y respectively.
Therefore;
½(3+x)(4+y)-42 = ½(xy)
12+3y+4x+xy-84 = xy
3y+4x = 72 --- (1).
3 ~ (3+x)
4 ~ (y+4)
Cross Multiply.
4(...
