Mathematics Question and Solution
Calculating length AB.
Let a be the radius of the inscribed semi circle.
b = 180-45
b = 135°
c² = 12²+5²-2*5*12cos45
c = 9.1731775442 units.
d = c+a
d = (9.1731775442+a) units.
e = 12+5
e = 17 units.
Calculating a.
17² = a²+(9.1731775442+a)²
289 = a²+84.1471862574+18.3463550884a+a²
2a²+18.3463550884a-204.8528137426 = 0
Resolving the quadratic equation.
a = 6.52481 units.
f = 2a+c
f = 2(6.52481)+9.1731775442
f = 22.2227975442 units
f is CD = AB.
AB = 22.2227975442 units.
