Given quadrilateral $ABCD$ with $AB=BC=CD$. Let $AC\cap BD=O$, $X,Y$ are symmetry points of $O$ respect to midpoints of $BC$, $AD$, and $Z$ is intersection point of lines, which perpendicular bisects of $AC$, $BD$. Prove that $X,Y,Z$ are collinear.
Source:
Tags: symmetry, geometry proposed, geometry
Given quadrilateral $ABCD$ with $AB=BC=CD$. Let $AC\cap BD=O$, $X,Y$ are symmetry points of $O$ respect to midpoints of $BC$, $AD$, and $Z$ is intersection point of lines, which perpendicular bisects of $AC$, $BD$. Prove that $X,Y,Z$ are collinear.