Mathematics Question and Solution
Notice.
Radius of the ascribed circle is 7 cm.
Calculating a, radius of the big inscribed circle.
(7-a)² = 2a²
49-14a+a² = 2a²
a²+14a-49 = 0
Resolving the above quadratic equation via completing the square approach.
(a+7)² = 49+(7²)
(a+7)² = 98
a = -7±√(98)
a = -7±7√(2)
It implies;
a ≠ -7-7√(2)
a = -7+7√(2)
a = 2.8994949366 cm.
b = 2(7)-a
b = 14-2.8994949366
b = 11.1005050634 cm.
b is the diameter of the orange circle.
c = ½(b)
c = ½(11.1005050634)
c = 5.5502525317 cm.
c is the radius of the orange circle.
Therefore, area orange circle is;
πc²
= π(5.5502525317)²
= 96.7777141166 cm²
= 96.78 cm² to 2 decimal places.
