MathNet 2015-part-04 — 191 problems (EN–VI) Question 35

For quadrilateral $ABCD$ we have $\angle A = \angle C = 90^{\circ}$. Let $E$ be a point inside the quadrilateral. Let $M$ be the midpoint of $BE$. Prove that $\angle ADB = \angle EDC$ if and only if $|MA| = |MC|$.