Triangle in circle -1

The problem

This is the first problem in the series.
Take any triangle ABC, the median AD, the angle bisector AE,
and the height AF meet the circumcircle ABC in points D, E, F:

Now assuming that we know points D, E, F,
how to construct the "parent" triangle ABC?

The hint

Start with line EO!

The answer

See here, but better try yourself!

The Solution

N/A