About an hour ago, I discovered a beautiful property of a parabola. If a circle intersects a parabola at four points, one of which is the vertex of the parabola, then the center of the triangle, whose vertices are the remaining three points, will belong to the axis of symmetry of the parabola
Is this feature known in advance or not, please mention any references that talk about the topic
I haven't tried to prove it yet, but I don't expect that to be difficult using analytic geometry, but evidence is welcome in the answers.