- Draw from the vertices of the tangential triangle parallels to the sides of ABC to build GIJ homothetic to ABC. Since BCF, CDA, AEB are isosceli the lines joining D, E, F with the circumcenter O of ABC are orthogonal to corresponding sides of GIJ and easily identified as its altitudes. Hence O is the orthocenter of GIJ.

- It follows that the circumcircle (c) of the tangential DEF is the Euler circle of GIJ, hence the circumcenter Q of DEF and O are on the Euler line of GIJ.

- The Euler lines of ABC and GIJ are parallel and have O in common, hence they coincide.

Orthic.html

Produced with EucliDraw© |