Mathematics Question and Solution
Let the radius of the ascribed circle be 2 units.
Therefore, radius of the bigger inscribed circle is 1 unit.
a = (1+y) units
b = (2-y) units.
c = (1-y) units.
Calculating y, radius of the big inscribed circle.
a² = c²+d²
(1+y)² = (1-y)²+d²
1+2y+y² = 1-2y+y²+d²
d² = 4y
d = √(4y)
d = 2√(y) units.
It implies;
d²+y² = b²
(2√(y))²+y² = (2-y)²
4y+y² = 4-4y+y²
8y = 4
y = ½ units.
Again, y is the radius of the big inscribed circle.
Recall.
d = 2√(y)
And y = ½ units.
d = 2√(½)
d = √(2) units.
e = 2+y
And y = ½ units.
e = 2+½
e = ½(5) units.
Therefore, the required angle x is;
tanx = d/e
x = atan(√(2)/(5/2))
x = atan(⅕(2√(2)))
x = 29.4962084966°
x ≈ 29.50° to 2 decimal places.
