Mathematics Question and Solution
Calculating r, radius of the red inscribed circle.
Notice.
40.5π units square is the area of the inscribed half circle.
½*x²π = 40.5π
πx² = 81π
x = 9 units.
x is the radius of the inscribed half circle.
a = 2x
a = 2*9 units.
a = 18 units
a is the radius of the ascribed quarter circle.
b = a-r
b = (18-r) units.
c²+r² = b²
c² = (18-r)²-r²
c = √((18-r)²-r²) units.
c = √(324-36r) units.
d = x+r
d = (9+r) units.
e = x-r
e = (9-r) units.
Calculating r.
d² = c²+e²
(9+r)² = √(324-36r)²+(9-r)²
81+18r+r² = 324-36r+81-18r+r²
18r = 324-36r-18r
72r = 324
r = 36/8
r = 9/2
r = 4.5 units.
Again, r is the radius of the inscribed red circle.
