# Further properties of Van Aubel Configuration

### Problem

Let $ABC$ be a triangle, $M_a$ the midpoint of $BC,$ $H$ the orthocenter of $\Delta ABC,$ $V_b,V_c,V'_b,V'_c$ the centers of the four squares, as in the diagram below:

Show that:

1. Six points $V_b,V'_b,M_a,H_a,V_c,V'_c$ lie on a circle.

2. $V_bV_c$ is a diameter of this circle.

3. Reflection $A'$ of $A$ in center of this circle is a fixed point, independent of $A.$

Note that this statement nicely complements van Aubel's theorem.