Mathematics Question and Solution
Calculating Area Inscribed Red Circle.
a = ½(8)
a = 4 units.
a is the radius of the two congruent half circles.
b = (4+x) units.
x is the radius of the red inscribed circle.
c = (4-x) units.
Therefore;
(4-x)² = x²+d²
16-8x+x²-x² = d²
d = √(16-8x) units.
e = 4+d
e = (4+√(16-8x)) units.
Calculating x.
(4+x)² = (4+√(16-8x))²+x²
16+8x+x² = 16+8√(16-8x)+16-8x+x²
16x = 16+8√(16-8x)
16x-16 = 8√(16-8x)
2x-2 = √(16-8x)
4x²-8x+4 = 16-8x
4x² = 12
x² = 3
x = √(3) units.
Again, x is the radius of the inscribed red circle.
Area red inscribed circle is;
πx²
= π√(3)²
= 3π square units.
