Mathematics Question and Solution
Calculating angle x.
Let the radius of the inscribed half circle be 1 unit.
Therefore, 2 units is the radius of the ascribed quarter circle.
a = (2-y) units.
b² = 1²+y²
b = √(1+y²) units.
b is BD.
c = 2(OB)
Where OB = 2 units, the radius of the ascribed quarter circle, and also the diameter of the inscribed half circle.
c = 2*2
c = 4 units.
c is double the radius of the ascribed quarter circle.
Calculate y.
It implies;
4 ~ √(1+y²)
√(1+y²) ~ y
Cross Multiply.
4y = √(1+y²)²
4y = 1+y²
y²-4y+1 = 0
(y-2)² = -1+(-2)²
(y-2)² = 3
y = 2±√(3)
It implies;
y ≠ 2+√(3) units.
y = (2-√(3)) units.
y = 0.26794919243 units.
tand = y/1
tand = (2-√(3))/1
d = atan(2-√(3))
d = 15°
Therefore, the required angle x is;
x = 90+d
x = 90+15
x = 105°
