[b]Proposition:[/b] [i]To Demonstrate that the opposite vertex lines of a hexagram circumscribed about a conic section pass through a point.[/i][br][br]Here is a construction of the Brianchon Point:.

Proof of this theorem is quite a challenge! Dorrie's relies heavily on projection theorems of Steiner and Desargues. For convenience, let a line joining opposite vertices of a hexagram be called a [i]Principal Diagonal[/i]. In the language of projection, the criterion we wish to establish is this:[br][br][i]It is always possible to construct a projection in which two of the Principal Diagonals are corresponding rays from projective centers, and the the third Diagonal as the axis of perspective upon which the two rays intersect[/i]. That is, the three Principal Diagonals meet at a single point.[br][br]_________________[br][b]Brianchon's Hexagram Theorem[/b][br]This is problem #62 in Heinrich Dorrie's [i]100 Great Problems of Elementary Mathematics[/i][br]More: [url]http://tube.geogebra.org/material/show/id/73813[/url][br][br]Used in: Conic from Five Tangents -- Drawing Solution: [url]http://tube.geogebra.org/material/show/id/337589[/url]