Mathematics Question and Solution
Calculating Area Blue Inscribed Circle.
Let a be the radius of the blue inscribed circle.
b = (a+5) cm.
c = 12-a-5
c = (7-a) cm.
d = (16-a-5)
d = (11-a) cm.
It implies;
(a+5)² = (7-a)²+(11-a)²
a²+10a+25 = 49-14a+a²+121-22a+a²
a²+10a+25 = 170-36a+2a²
a²-46a+145 = 0
(a-23)² = -145+(-23)²
(a-23)² = 384
a = 23±√(384)
a = 23±8√(6)
It implies;
a ≠ 23+8√(6) units.
a = 23-8√(6) units.
a = 3.40408205773 units.
Area Blue Inscribed Circle is;
πa²
= π(23-8√(6))²
= 36.4040677301 square units.
