Mathematics Question and Solution
Calculating Length x.
Notice.
AC = BC.
a²+a² = 2²
2a² = 4
a² = 2
a = √(2) units.
a is AC = BC.
b = a-y
b = (√(2)-y)
y is the radius of the green circle.
c = y+y+x
c = (2y+x) units.
Where c is equal to a.
Calculating y.
y²+y² = b²
2y² = (√(2)-y)²
2y² = 2-2√(2)y+y²
y²+2√(2)y-2 = 0
(y+√(2))² = 2+√(2)²
(y+√(2))² = 4
y = -√(2)±√(4)
y = -√(2)±2
It implies;
y ≠ (-√(2)-2) units.
y = (2-√(2)) units.
Again, x is the radius of the green circle.
Recall.
c = a = (2y+x) units.
And a = √(2) units while y = (2-√(2)) units.
Therefore;
Calculating x.
√(2) = 2(2-√(2)+x
√(2) = 4-2√(2)+x
x = √(2)+2√(2)-4
x = (3√(2)-4) units.
x = 0.24264068712 units.
