Mathematics Question and Solution
Calculating r, radius of the yellow inscribed circle.
Notice.
OB = 16, radius of the ascribed quarter circle.
OM = AM.
It implies;
OM = AM = ½(16)
OM = AM = 8 units.
OM = AM = diameter of the inscribed red half circle.
a = ½(AM)
a = ½(8)
a = 4 units.
a is the radius of the red inscribed half circle.
b = (r+4) units.
c = (16-r) units.
d = 16-4-r
d = (12-r) units.
It implies;
c² = e²+r²
(16-r)² = e²+r²
256-32r+r² = e²+r²
256-32r = e²
e = √(256-32r) units.
Therefore r, radius of the inscribed yellow circle is;
e²+d² = b²
√(256-32r)²+(12-r)² = (r+4)²
256-32r+144-24r+r² = r²+8r+16
256-32r+144-24r = 8r+16
384 = 64r
r = 96/16
r = 6 units.
