Mathematics Question and Solution
Calculating R, radius of the inscribed yellow circle.
a = ¼(180)
a = 45°
b = 180-a
b = 135°
c = ½(a)
c = 22.5°
d = b-c
d = 135-22.5al
d = 112.5°
e = 180-a-d
e = 180-45-112.5
e = 22.5°
tan22.5 = 2/f
f = 4.82842712475 units.
g² = f²+2²
g = √(4.82842712475²+2²)
g = 5.22625185951 units.
g is the diameter of the inscribed half circle.
h = ½(g)
h = 2.61312592975 units.
h is the radius of the inscribed half circle.
tan(0.5*22.5) = R/j
j = 5.02733949213R units.
k = j-h
k = (5.02733949213R-2.61312592975) units.
l = h-R
l = (2.61312592975-R) units.
It implies, R, the radius of the inscribed yellow circle is;
l² = R²+k²
(2.61312592975-R)² = R²+(5.02733949213R-2.61312592975)²
Therefore;
R = 0.83278357 units.
Again, R is the radius of the inscribed yellow circle.
