Mathematics Question and Solution
Calculating R, radius of the circle.
Let alpha be x.
y² = 11²+37²-2*11*37cosx
y² = 1490-814cosx --- (1).
y² = 26²+37²-2*26*37cosx
y² = 2045-1924cosx --- (2).
Equating (1) and (2).
1490-814cosx = 2045-1924cosx
1924cosx-814cosx = 2045-1490
1110cosx = 555
x = acos(555/1110)
x = acos(½)
x = 60°
Again, x is alpha.
Recall.
At (1).
y² = 1490-814cosx
And x = 60°
y² = 1490-407
y = √(1490-407)
y = 19√(3) units.
y = 32.9089653438 units.
It implies, R, radius of the circle is;
sin60 = (0.5y)/R
R = (0.5*32.9089653438)/sin60
R = (0.5*19√(3))/(√(3)/2)
R = 19 units.
