Symmetric_triangles3

Perspective triangles inscribed in a conic

If two triangles, inscribed in a conic are perspective, then their perspectivity axis and center are related by the polar-pole relation of that conic. This is a particular kind of perspectivity.
How can one recognize directly this kind of perspectivity, from other properties of a pair of perspective triangles? Notice that, in general, the vertices of two perspective triangles are not contained in a conic.

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