MathNet 2019-part-01 — 184 problems (EN–VI) Question 129

The diagonals of the inscribed quadrilateral $ABCD$ intersect at the point $O$. The points $P$, $Q$, $R$ and $S$ are the feet of the perpendiculars from $O$ to the sides $AB$, $BC$, $CD$ and $DA$ respectively.
Prove the inequality $BD \ge SP + QR$.