# Some properties of a regular nonagon

- Author:
- Zoltán Kovács

In the figure a regular nonagon and a regular triangle

*ABO*are given.*J*and*K*are midpoints of two neighbor sides of the nonagon.*L*is the midpoint of the nonagon,*N*is the midpoint of the arc*AI*of the circumcircle of the nonagon. Finally,*M*is the midpoint of the radius*LN*. Prove that*JM*is parallel to*OB*. This is one formulation of Karst's statement. GeoGebra can find an automatic proof by comparing*JM*and*OB*with the Relation tool. (As of August 2018 this statement cannot be completely proven with GeoGebra, just a numerical check can be performed.)