Mathematics Question and Solution
Let AB, the side length of the square be 1 unit.
a² = 1²+1²
a = √(2) units.
b²+1² = c²
c = √(b²+1) units.
b is the radius of the inscribed circle.
d² = 2b²
d = √(2)b units.
It implies;
c+d = a
√(b²+1)+√(2)b = √(2)
b²+1 = (√(2)-√(2)b)²
b²+1 = 2-4b+2b²
b²-4b+1 = 0
Resolving the above quadratic equation via completing the square approach to get b, radius of the circle.
(b-2)² = -1+(-2)²
(b-2)² = 3
b = 2±√(3)
It implies;
b ≠ 2+√(3)
b = (2-√(3)) units.
b = 0.2679491924 units.
tanc = 0.2679491924/1
c = atan(0.2679491924)
c = 15°
It implies, the required angle, x is;
x = 45+c
x = 60°
