The extensions of sides $AB$ and $CD$ of a convex quadrilateral $ABCD$ intersect at $K$. It is known that $AD = BC$. Let $M$ and $N$ be the midpoints of sides $AB$ and $CD$. Prove that the triangle $MNK$ is obtuse. (5 points)
Source: Fall 2005 Tournament of Towns Junior A-Level #2
Tags: geometry
The extensions of sides $AB$ and $CD$ of a convex quadrilateral $ABCD$ intersect at $K$. It is known that $AD = BC$. Let $M$ and $N$ be the midpoints of sides $AB$ and $CD$. Prove that the triangle $MNK$ is obtuse. (5 points)