Mathematics Question and Solution
Calculating r, radius of the circle.
Let theta be x.
Notice.
BC = CD, let it be a.
a² = 2²+13²-2*2*13cosx
a² = 173-52cosx --- (1).
a² = 11²+13²-2*11*13cosx
a² = 290-286cosx --- (2).
Calculating x.
Equation (1) and (2).
173-52cosx = 290-286cosx
234cosx = 117
cosx = ½
x = 60°
Calculating a.
Substituting x in (1).
a² = 173-52cos60
a² = 173-26
a = √(147) units.
Therefore, r is;
sin60 = ½√(147)/r
√(3)r = √(147)
r = 7 units.
