MathNet 2010 — Part 05 Question 173

Let $AMNB$ be a quadrilateral inscribed in a semicircle of diameter $AB = x$. Denote $AM = a$, $MN = b$, $NB = c$. Prove that
$$
x^{3} - (a^{2} + b^{2} + c^{2})x - 2abc = 0.
$$