Problem

Source: 2018 USAJMO #4

Tags: AMC, USA(J)MO, USAJMO, 2018 USAJMO Problem 4



Triangle $ABC$ is inscribed in a circle of radius 2 with $\angle ABC \geq 90^\circ$, and $x$ is a real number satisfying the equation $x^4 + ax^3 + bx^2 + cx + 1 = 0$, where $a=BC$, $b=CA$, $c=AB$. Find all possible values of $x$.