Mathematics Question and Solution
Calculating r, radius of the half circle.
a²+9² = 23²
a = 8√(7) units.
a = 21.1660104885 units.
tanb = 8√(7)/8
b = atan(8√(7)/9)°
c = (r-5) units.
(r-5)² = d²+(½*8√(7))²
r²-10r+25 = d²+112
d = √(r²-10r-87) units.
e = (9+√(r²-10r-87)) units.
Calculating r.
(½*8√(7))²+(9+√(r²-10r-87))² = r²
112 +81+18√(r²-10r-87)+r²-10r-87 = r²
106+18√(r²-10r-87)-10r = 0
18√(r²-10r-87) = 10r-106
324(r²-10r-87) = 100r²-2120r+11236
324r²-3240r-28188 = 100r²-2120r+11236
224r²-1120r-39424 = 0
28r²-140r-4928 = 0
4r²-20r-704 = 0
r²-5r-176 = 0
r²-16r+11r-176 = 0
r(r-16)+11(r-16) = 0
(r-16)(r+11) = 0
It implies;
r ≠ -11 units.
r = 16 units.
