Mathematics Question and Solution
Calculating Angle x.
Let 2 units be the radius of the ascribed quarter circle and a be the radius of the inscribed circle.
Calculating a.
b = (2-a) units.
It implies;
2a² = (2-a)²
2a² = 4-4a+a²
a²+4a-4 = 0
(a+2)² = 8
a = -2±√(8)
It implies;
a = (2√(2)-2) units.
a = 0.82842712475 units.
Again, a is the radius of the inscribed circle.
tanc = 2/0.82842712475
c = 67.4999999999
c = 67.5°
d = 90-c
d = 90-67.5
d = 22.5°
Therefore, the required angle, x is;
x = d+45
x = 22.5+45
x = 67.5°
