MathNet 2008-part-02 — 165 problems (EN–VI) Question 53

Let $AB$ be a chord of a circle and let $P$ be a point inside segment $AB$ such that $AP = 2PB$. Let $DE$ be the chord through $P$ perpendicular to $AB$. Prove that the midpoint $Q$ of $AP$ is the orthocenter of $ADE$.