Mathematics Question and Solution
Calculating length d.
Notice.
3 units is the radius of the inscribed green circle.
6 units is the radius of the inscribed purple circle.
9 units is the radius of the ascribed blue circle.
a = 6-3
a = 3 units.
b =9+9-3-6
b = 9 units.
c²+3² = 9²
c² = 81-9
c = √(72)
c² = 6√(2) units.
x ~ 6√(2)
6 ~ 9
Cross Multiply.
9x = 36√(2)
x = 4√(2) units.
4√(2) ~ 6√(2)
e ~ 3
2 ~ 3
e ~ 3
Cross Multiply.
3e = 6
e = 2 units.
f = 3+e
f = 5 units.
g²+5² = 9²
g² = 81-25
g = √(56)
g = 2√(14) units.
Therefore, length d is;
d = 2g
d = 2*2√(14)
d = 4√(14) units.
d = 14.9666295471 units.
d ≈ 15 units to 1 decimal place.
Or
cosh = 5/9
h = acos(5/9)°
j = 2h
j = 2acos(5/9)°
Therefore; length d is;
d² = 9²+9²-2*9*9cos(2acos(5/9))
d² = 224
d = √(224)
d = √(16*14)
d = 4√(14) units.
d = 14.9666295471 units.
d ≈ 15 units to 1 decimal place.
