Solutions to cosine rule
Shows that any triangle with one angle and two sides invariant has at most 2 solutions.
These solutions lie on a circle, and are real due to the solution of the cosine rule equation, quadratic in x.
x^2 + 2bcos(theta) x (b^2- c^2) = 0
where b and c are the fixed sides of a triangle, and theta is the fixed angle.
x is the variable other side.