KöMaL 2016 C1334

Given that the cyclic quadrilateral $ABCD$ is either a trapezium (where $AB\parallel CD$ ) or its side $AB$ is a diameter of the circumscribed circle, then the equations $BD\cdot x+AD\cdot \sqrt{1-x^2} = AC;$ $AC\cdot x+BC\cdot \sqrt{1-x^2} = BD$ are held for some $x$ of $0<x<1$.