true.
Brianchon’s theorem
Brianchon’s theorem was discovered much later by the French mathematician
and chemist Charles-Julien Brianchon. Let’s draw six tangents that we’ll call the
lines a 1 , b 1 and c 1 and a 2 , b 2 and c 2 , touching the circumference of an ellipse. Next
we can define three diagonals, the lines p, q and r, by the meeting of lines, so
that: p is the line between the points where a 1 meets b 2 and where a 2 meets b 1 ; q
is the line between the points where a 1 meets c 2 and a 2 meets c 1 ; and r is the line
between the points where b 1 meets c 2 and b 2 meets c 1. Brianchons’s theorem
states that lines p, q and r meet at a point.
These two theorems are dual to each other, and it is another instance of the
theorems of projective geometry occurring in pairs.