Mathematics Question and Solution
Notice!
Radius of the big inscribed green circle is 4 units.
Let the radius of the small inscribed circle be a.
Calculating a.
b = (4+a) units.
c = (4-a) units.
d = (5-a) units.
It implies;
(4+a)² = (4-a)²+(5-a)²
16+8a+a² = 16-8a+a²+25-10a+a²
16a = 25-10a+a²
a²-26a+25 = 0
a²-a-25a+25 = 0
a(a-1)-25(a-1) = 0
Therefore;
(a-1)(a-25) = 0
It implies;
a = 1 unit.
Area Green is;
π(4²)+π(1²)
= 16π+π
= 17π square units.
