Mathematics Question and Solution
Let R be radius of the quarter circle.
Let r be radius of the inscribed circle.
R will be;
√(3²+4²)
R=√(25)
R= 5 unit.
Calculating r, radius of the inscribed circle.
Therefore r will be;
(5-r)²=(3+r)²+r²
25-10r+r²=9+6r+r²+r²
r²+16r-16=0
Therefore resolving the quadratic equation via completing the square side to get r, radius of the inscribed circle.
(r+8)² = 16+8²
(r+8)² = 80
r = -8±√(80)
r = -8±4√(5)
It implies;
r ≠ -8-4√(5)
r = -8+4√(5)
r = 4(√(5)-2) units.
r = 0.94427191 units.
