Mathematics Question and Solution
Calculating length BA, diameter of the small half circle.
a = 3+12+5
a = 20 units.
a is the diameter of the big half circle.
b = ½(a)
b = ½(20)
b = 10 units.
b is the radius of the big half circle.
Let x be the radius of the small half circle.
c²+x² = 10²
c² = 100-x²
c = √(100-x²) units.
d = ½(12)
d = 6 units.
x² = 6²+e²
e² = x²-36
e = √(x²-36) units.
f = 10-3-6
f = 1 unit.
It implies, x is;
e²+f² = c²
√(x²-36)²+1² = √(100-x²)²
x²-36+1 = 100-x²
2x² = 100+35
x² = ½(135)
x = √(67.5) units.
Again, x is the radius of the small half circle (half BA).
It implies, length BA is;
2x
= 2√(67.5) units.
= 16.4316767252 units.
