Mathematics Question and Solution
Calculating Length EF (x).
Let a be the radius of the inscribed blue half circle.
b = (4+a) units.
Calculating a.
8²+a² = (4+a)²
64+a² = 16+8a+a²
48 = 8a
a = 6 units.
Again, a is the radius of the blue inscribed half circle.
c = 2a
c = 2(6)
c = 12 units.
c is BC, the diameter of the blue inscribed half circle.
d = AB+BC+CD
d = 4+12+9
d = 25 units.
d is AD, the diameter of the ascribed half circle.
cose = 8/10
e = acos(4/5)°
f = (8+x) units.
Calculating x.
cos(acos(4/5)) = (8+x)/25
(4/5) = (8+x)/25
100 = 40+5x
5x = 60
x = 12 units.
