Mathematics Question and Solution
Calculating x.
Notice!
Diameter of the ascribed circle is 10 cm.
It's radius, a is;
a = ½(10)
a = 5 cm.
Let b be the radius of the inscribed circle.
c = b-4
c = 1 cm.
d = (5-b) cm.
It implies;
Calculating b, radius of the inscribed circle.
(5-b)² = b²+1
25-10b+b² = b²+1
10b = 24
b = 2.4 cm.
Again, b is the radius of the inscribed circle.
tane = 1/2.4
e = atan(1/2.4)°
e = 22.619864948°
f = 180-e
f = 157.380135052°
Therefore, the required length, x is;
tan(0.5f) = (x/b)
tan(0.5*157.380135052) = x/(2.4)
x = 2.4tan(0.5*157.380135052)
x = 2.4*5
x = 12 cm.
