Fig. 5
From: Nets of Lines with the Combinatorics of the Square Grid and with Touching Inscribed Conics
The points \(p_{1,2}, p_{2,3},p_{3,4},p_{4,1}\) are the tangency points of an inscribed conic. Lemma 2.5 defines an inscribed conic with tangency points \(q_{1,2},q_{2,3},q_{3,4},q_{4,1}\) such that \(q_{1,2},q_{3,4},p_{2,3},p_{4,1}\) are collinear and \(q_{2,3},q_{4,1},p_{1,2},p_{3,4}\) are collinear