The reflected on AC line EY and the reflected on AB line FD pass correspondingly from the reflected of H on the respective sides, points E, F on the circumcircle (see Orthocenter.html ).

The angle of these lines at Y is equal to the corresponding angle(FDE) of the triangle DEF, formed by the reflections of H on the sides of ABC. This follows by measuring the angles:

and using the well known properties of DEF (ibid). Letting the variable line HX pass not through H but through an arbitrary fixed point H', yields another interesting configuration studied in OrthicAndPedal.html .

OrthicAndPedal.html

SteinerLine.html

Produced with EucliDraw© |