# Solutions to Problems 1043-1050

Q1043. An equilateral triangle $APQ$ is drawn so that $P,Q$ are on the sides $BC$ and $DC$ of a square $ABCD,$ with $|AP| =|AQ|.$ Show that the perimeter of $APQ$ is less than the perimeter of the triangle $ABD$ (unless $P$ is at $B$ and $Q$ is at $D$).