[2] The tangents to the circumcircle of an equilateral triangle DEF are the trilinear polars of the points at infinity with respect to the anticomplementary triangle ABC of DEF.

[3] The two tangents L

[1] and [2] are proved in IncircleTangents.html . The parallelity in [3] is a consequence of the fact that the two triangles DEF and ABC are anti-homothetic with respect to their common center and with homothety ratio 2. The constancy of the distance of these parallels is obvious from the fact that they are tangent to two concentric circles. From there also follows the claim on the value of this distance.

For a generalization of this property to arbitrary triangles see the discussion (especially [6]) in TriangleConics.html .

IncircleTangents.html

TriangleConics.html

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