An unequal acute-angled triangle $ABC$ with an orthocenter $H$ is given, $M$ is the midpoint of side $BC$. Points $K$ and $L$ lie on a line passing through $H$ and perpendicular to $AM$ such a $KB$ and $LC$ perpendicular to $BC$. Point $N$ lies on the line $HM$, and the lines $AN$ and $AH$ are symmetric with respect to the line $AM$. Prove that a circle with a diameter $AN$ touches two circles: centered at $K$ and with a radius $KB$ and with a center $L$ and radius $LC$.