MathNet 2015-part-02 — 191 problems (EN–VI) Question 98

For a trapezoid $ABCD$ ($AB \parallel CD$) it holds $BC = AB + CD$. Prove that
(i) there is a point of a circle with diameter $BC$ on the leg $AD$,
(ii) there is a point of a circle with diameter $AD$ on the leg $BC$.