[1] Their axes are parallel to the medians of triangle ABC.

[2] Parabola p

[3] Their focal points coincide with the vertices of the second Brocard triangle of ABC.

[4] Every pair of parabolas has an intersection point on the median which is parallel to the axis of the third parabola.

[5] The three intersection points A',B',C' of [4] define a triangle homothetic to DEF with respect to the centroid J of ABC and with a homothety ratio equal to 2/3.

[6] The tangent to parabola p

Artzt parabolas of 2nd kind are discussed in the file Artzt2.html .

[1,2] Follow from general facts on parabolas. Parabola p

The precise location of points B', C' on the diagonals of trapezium FECB is discussed in the file ParabolaTrapezium.html .

Artzt2.html

ArtztSteiner.html

BrocardSecond.html

Parabola.html

ParabolaTrapezium.html

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