Problem 1: Let $ABCD$ be a parallelogram. Construct four squares on the sidelines $ABCD$. Let $NPMO$ be the Thebault’s square. Show that:
1-Centers of four circles $(NAP)$, $(PBM)$, $(MCO)$, $(OCN)$ is rhombus.
2-Intersection of four circles $(NAP)$ and $(PBM)$, $(PBM)$ and $(MCO)$, $(MCO)$ and $(OCN)$, $(OCN)$ and $(NAP)$ form a square.
Problem 2: $ABCD$ be a parallelogram, construct for square on the sidelines of ABCD. Show that $OPMN$ be a rectangle.
Problem 3: Let $A, B, C, D$ lie on a circle with center $(O)$. Construct four squares on the sidelines $ABCD$. Let $PMNQ$ be the van Aubel 's equidiagonal orthodiagonal quadrilateral. Show that:
1-Six circles $(QAP)$, $(PBM)$, $(MCN)$, $(NDQ)$, $(PON)$, $(MOQ)$ are concurrent be a point.
2-Centers of four circles $(QAP)$, $(PBM)$, $(MCN)$, $(NDQ)$ lie on a circle.
3-Center of four circles $(QOP)$, $(POM)$, $(MON)$, $(NOQ)$ lie on a circle.
