MathNet 2015-part-06 — 191 problems (EN–VI) Question 178

Let $ABC$ be an acute-angled triangle and let the altitudes $AA_1$ and $BB_1$ intersect at $H$. Consider the circles $w_1$ and $w_2$ with centers $H$ and $B$ and with radii $HB_1$ and $BB_1$ respectively. Let $CN$ and $CK$ be the tangent lines from $C$ to the circles $w_1$ and $w_2$ respectively $(N \neq B_1, K \neq B_1)$. Prove that $A_1, N$ and $K$ are collinear.
(Igor Nagel)