Mathematics Question and Solution
Notice.
r, radius of the ascribed half circle is 5 units.
Calculating the area of the inscribed red circle.
Let it's radius be x.
Calculating x.
a = (5-x) units.
tan15 = x/b
b = (x/tan15) units.
c = b-5
c = ((x/tan15)-5) units.
It implies;
a² = c²+x²
(5-x)² = ((x/tan15)-5)²+x²
25-10x+x² = (x²/(tan15)²)-(10x/tan15)+25+x²
-10x = (x²/(tan15)²)-(10x/tan15)
(10x/tan15)-10x = (x²/(tan15)²)
(10/tan15)-10 = (x/(tan15)²)
x = 10tan15-10(tan15)²
x = 1.96152422707 units.
Therefore area shaded red is;
πx²
= π(1.96152422707)²
= 12.087520559 square units.
