Mathematics Question and Solution
r = √(3²+4²)
r = 5 units.
r is the radius of the quarter circle.
(5-x)² = x²+(3+x)²
x is the radius of the inscribed yellow circle.
Therefore;
25-10x+x² = x²+9+6x+x²
x²+16x-16 = 0
(x+8)² = 16+64
x = -8±√(80)
x = -8±4√(5)
Therefore;
x ≠ -8-4√(5)
x = -8+4√(5)
x = 4√(5)-8 units.
x = 0.94427191 units.
Area yellow Inscribed circle is;
πx²
= π(4√(5)-8)²
= 80-64√(5)+64
= (144-64√(5))π square units.
= 16π(9-4√(5)) square units.
= 0.89164944001π square units.
