Mathematics Question and Solution
Let a be the diameter of the semi circle.
a² = b²+14²
b² = a²-196
b = √(a²-196)
It implies;
b² = 6²+6²-2*6*6(-cosc)
a²-196 = 72+72cosc
a²-196-72 = 72cosc
72cosc = a²-268
cosc = (a²-268)/72 --- (1).
cosc = 14/a --- (2).
Equating (1) and (2).
cosc = cosc
(a²-268)/72 = 14/a
a³-268a = 1008
a³-268a-1008 = 0
Resolving the polynomial equation.
a = 18 units.
It implies;
Radius, r of the semi circle is;
½(a)
= ½(18)
= 9 units.
