Tessellate S.T.E.M.S. (2019) - Mathematics - Category B - Set 2 - Objective Problem 4

Let $AB$ be a chord of length $2018$ inside a circle of radius $2019$ . Let $AB$ be bisected at $P$ . $CD$ is another chord of the circle which passes through $P$ . Let the perpendicular to $CD$ at $P$ meet the semicircle with diameter $CD$ at $Q$ . Find $PQ$ .

This problem is a part of Tessellate S.T.E.M.S. (2019)