Question 76
Let $AA_1$, $BB_1$ be the altitudes of an acute non-isosceles triangle $ABC$. The circumcircle of triangle $ABC$ meets that of triangle $A_1B_1C$ at point $N$ (different from $C$). Let $M$ be the midpoint of $AB$ and $K$ be the intersection point of $CN$ and $AB$.
Prove that the line of centers of the circumcircles of triangles $ABC$ and $KMC$ is parallel to the line $AB$.
Prove that the line of centers of the circumcircles of triangles $ABC$ and $KMC$ is parallel to the line $AB$.