[alogo] 1. Brianchon's theorem for circumscriptible hexagons

In every circumscriptible in a conic hexagon, the diagonals, joining opposite vertices, pass through a common point O.

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[alogo] 2. Brianchon's theorem for circumscriptible pentagons

For every circumscriptible pentagon the line (AL, look at [concurring-1]) joining a vertex to the contact point of the opposite side and the two diagonals (CE and DB ) from the end points of that side to the neighbour vertices of the initial vertex (A) intersect at a point (U).

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[alogo] 3. Brianchon's theorem for circumscriptible quadrilaterals

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The diagonals and the lines joining opposite contact-points, in a circumscriptible to a conic quadrilateral, pass all through a common point E. Look at Brianchon.html for the proof in the case of circles.

[alogo] 4. Brianchon's theorem for circumscriptible triangles


The lines joining a vertex with the contact point of the opposite side of a triangle circumscribed to a conic pass all through a common point E. This is a basic property of this kind of conics and E is called the perspector of the conic. Each point E not lying on the side-lines of the triangle uniquely defines a corresponding inscribed conic. This subject is investigated in TriangleConics.html .

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