GR-HMS 2020 Problem 2

Given a line segment $AB$ and a point $C$ lies inside it such that $AB=3 \cdot AC$ . Construct a parallelogram $ACDE$ such that $AC=DE=CE>AR$ . Let $Z$ be a point on $AC$ such that $\angle AEZ=\angle ACE =\omega$ . Prove that the line passing through point $B$ and perpendicular on side $EC$ , and the line passing through point $D$ and perpendicular on side $AB$ , intersect on point , let it be $K$ , lying on line $EZ$ .