Mathematics Question and Solution
Calculating FM ÷ ML.
Let 2 units be the side length of square.
Calculating FM.
tana = 2/1
a = atan(2)°
a is angle AFB.
Let b, be the radius of the small inscribed circle.
c = (1-b) units.
Therefore;
Calculating b.
tan(½atan(2)) = b/(1-b)
b = 0.6180339887(1-b)
1.6180339887b = 0.6180339887
b = 0.3819660112 units.
Again, b is the small inscribed circle radius.
It implies;
c = 1-0.3819660112
c = 0.6180339888 units.
c is FM.
Calculating ML.
Let d, be the radius of the big inscribed circle.
e = (2-d) units.
Therefore;
tan(½atan(2)) = d/(2-d)
d = 0.6180339887(2-d)
1.6180339887d = 1.2360679774
d = 0.7639320225 units.
Again, d is the big inscribed circle radius.
It implies;
e = 2-d
e = 2-0.7639320225
e = 1.2360679775 units.
e is AL.
f² = 2²+1²
f = √(5) units.
f is AF.
g = f-e-c
g = 0.3819660112 units.
g is ML.
Therefore;
FM ÷ ML is;
0.6180339888÷0.3819660112
= 1.6180339893
= ½(1+√(5))
