Question 77
The hexagon $ABCDEF$ is cyclic and the distance between the midpoints of the sides $[BC]$ and $[EF]$ is equal to $\frac{AD}{2}$. Denote $H_1, H_2, H_3$ and $H_4$ the orthocenters of the triangles $ABC$, $BCD$, $DEF$ and, respectively, $EFA$. Show that the quadrilateral $H_1H_2H_3H_4$ is a rhombus.
Traian Tămâian
Traian Tămâian