Mathematics Question and Solution
Let a be the radius of the inscribed orange circle.
(3+a)² = a²+b²
b² = 9+6a+a²-a²
b = √(9+6a) cm.
c = c-3
c = (√(9+6a)-3) cm.
It implies;
(6-a)² = a²+c²
(6-a)² = a²+(√(9+6a)-3)²
36-12a+a² = a²+9+6a-6√(9+6a)+9
36-12a = 18+6a-6√(9+6a)
6√(9+6a) = 18a-18
√(9+6a) = 3a-3
9+6a = 9a²-18a+9
0 = 9a²-24a
9a = 24
3a = 8
a = (8/3) cm.
Again, a is the radius of the inscribed orange circle.
Area inscribed orange circle is;
πa²
= π(8/3)²
= ⅑(64)π cm²
= 22.3402144255 cm²
