Mathematics Question and Solution
Calculating the area of the inscribed circle.
Notice.
The inscribed triangle is equilateral.
Let x be the radius of the inscribed circle.
a = (12-x) cm.
It implies;
tan30 = x/(12-x)
√(3)x = 12-x
x(1+√(3)) = 12
x = 12/(1+√(3))
x = (12-12√(3))/(-2)
x = (6√(3)-6) cm.
x = 4.39230484541 cm.
Again, x is the radius of the inscribed circle.
Therefore, area inscribed circle is;
πr²
= π(6√(3)-6)²
= (144-72√(3))π
= 72π(2-√(3)) cm²
