Question 59
The angles at the vertices $A$ and $C$ in the convex quadrilateral $ABCD$ are not acute. Points $K, L, M$ and $N$ are marked on the sides $AB, BC, CD$ and $DA$ respectively.
Prove that the perimeter of $KLMN$ is not less than the double length of the diagonal $AC$.
Prove that the perimeter of $KLMN$ is not less than the double length of the diagonal $AC$.