Question 59
Let $ABCD$ be a trapezium with a major base $AB$ such that the diagonals $AC$ and $BD$ are perpendicular. Let $O$ be the center of the circumference circumscribed to the triangle $ABC$ and let $E$ be the point of intersection between the straight line $OB$ and the straight line $CD$. Prove that
$$
\overline{BC}^2 = \overline{CD} \cdot \overline{CE}
$$
$$
\overline{BC}^2 = \overline{CD} \cdot \overline{CE}
$$