Let a be the radius of the circ.
Calculating a.
b = ½(12+2)
b = 7 units.
c = ½(4+6)
c = 5 units.
d = b-2
d = 7-2
d = 5 units.
It implies;
a² = c²+d²
a = √(5²+5²)
a = √(50)...
Let a be the radius of the white inscribed circle.
b = (10-a) units.
Calculating a.
b² = a²+5²
(10-a)² = a²+25
100-20a+a² = a²+25
75 = 20a
a = ¼(15) units.
a = 3.75 units.
c = ½(10)
c = 5 units...
Let a be the radius of the half circle.
b = (a-1) units.
c²+1² = b²
c² = a²-2a+1-1
c = √(a²-2a) units.
d = a+c
d = (a+√(a²-2a)) units.
d is the required length.
e = (a+1) units....
x+a = y+2a
4+a = 3+2a
a = 1 unit.
It could be;
a = √(4²+3²)-4
a = 5-4
a = 1 unit.
Or
2a = √(4²+3²)-3
2a = 5-3
a = 1 unit.
Which makes;
b = y+a
b = 4+a
And a = 1 unit.
b = 5 units.
Or
b = y+2a
b =...
c² = 5³+12²
c = √(169)
c = 13 units.
Calculating a, radius of the inscribed yellow circle.
5a+12a+13a = (12*5)
30a = 60
a = 2 units.
Calculating b, radius of the blue inscribed circle....
a²+m² = 12²
a = √(144-m²) units.
Calculating m.
(4m)² = (3m)²+√(144-m²)²
16m² = 9m²+144-m²
8m² = 144
2m² = 36
m² = 18
m = 3√(2) units.
Recall.
a = √(144-m²)
And m = 3√(2) units.
a = √(144-(3√(2)...
Notice.
4 units is the radius of the inscribed circle.
a² = 2(4)²
a = 4√(2) units.
8² = (4√(2))²+4²-2*4*4√(2)cosb
64 = 32+16-32√(2)cosb
32√(2)cosb = 48-64
cosb = -16/(32√(2))
b = acos(-1/(2√(2)))...
a²+9² = 15²
a = √(15²-9²)
a = 12 units.
a is AF.
c = (9-b) units.
Therefore;
12 ~ b
9 ~ (9-b)
Cross Multiply.
108-12b = 9b
21b = 108
b = ⅐(36) units.
b is the radius of the inscribed half circl...
Calculating x, length DE.
a = ½(6)+x
a = (3+x) units.
Therefore;
Length DE, x is;
a = 8
3+x = 8
x= 8-3
x = 5 units.
Calculating yellow area.
It implies;
2a² = 4²
Where a is the height of the yellow area.
Therefore;
2a² = 4²
2a² = 16
a² = 8
a = √(8)
a = 2√(2) units.
Area Yellow is;
½*a*6
=...
