Question 64
In a convex quadrilateral $ABCD$ let $M$ and $N$ be midpoints of sides $AD$ and $BC$, respectively. Points $K$ and $L$ are chosen on sides $AB$ and $CD$, respectively, in such a manner that $\angle MKA = \angle NLC$. Prove that if lines $BD$, $KM$ and $LN$ meet at one point, then
$$
\angle KMN = \angle BDC, \quad \angle LNM = \angle ABD
$$
$$
\angle KMN = \angle BDC, \quad \angle LNM = \angle ABD
$$