Mathematics Question and Solution
Calculating Area Red.
a = 1+(161/9)+(10/9)
a= 1+(171/9)
a = 1+19
a = 20 units.
a is the diameter of the ascribed circle.
b = ½(a)
b = 10 units.
b is the radius of the ascribed circle.
Let x be the radius of the inscribed circle.
c = (10-x) units.
d = 10-1
d = 9 units.
It implies;
(10-x)² = x²+9²-2*9*xcosy
100-20x+x² = x²+81-18xcosy
81xcosy = 20x-19
cosy = (20x-19)/(18x) --- (1).
cosy = (161/9)/(2x) --- (2).
Calculating x.
Equating (1) and (2).
(20x-19)/(18x) = (161/9)/(2x)
2(20x-19) = (161/9)*18
40x-38 = 322
40x = 360
4x = 36
x = 9 units
Again, x is the radius of the inscribed circle.
Therefore, Area Red is;
πb²-πx²
= π(10)²-π(9)²
= (100-81)π
= 19π square units.
