MathNet 2021 — Part 09 Question 3

Let $ABCD$ be a rhombus with center $O$, and let $P$ lie on side $AB$. Let $I,J,L$ be the incenters of $PCD,PAD,PBC$, respectively. Let $H,K$ be the orthocenters of $PLB,PJA$, respectively. Prove that $OI\perp HK$.