MathNet 2020 — Math Olympiad Vault — Part 06 Question 97

Define $H_a$, $H_b$, $H_c$ as projections of $A$, $B$, $C$ on $BC$, $AC$, $AB$ respectively. $H$ is the orthocenter of $\triangle ABC$ and $K$ is a reflection of $A$ over $BC$. The line parallel to $H_bH_c$ through $H$ meets $AB$ and $AC$ in points $X$ and $Y$. Prove that inscribed circles of $\triangle ABC$ and $\triangle XYK$ touch.
(Michael Bondarenko)