Tangential quadrilateral all of whose sides are tangent to a single conic section has three diagonals that meet at a point. From a tangential quadrilateral, one can form a hexagon with two 180° angles, by placing two new vertices at two opposite points of tangency; all six of the sides of this hexagon lie on lines tangent to the inscribed circle, so its diagonals meet at a point. But two of these diagonals are the same as the diagonals of the tangential quadrilateral, and the third diagonal of the hexagon is the line through two opposite points of tangency. Repeating this same
Peptide plane flipping Peptide plane flipping Peptide plane flipping is a type of conformational change that can occur in proteins by which the dihedral angles of adjacent amino acids undergo large-scale rotations with little displacement of the side chains. The plane flip is defined as a rotation of the dihedral angles φ,ψ at amino acids "i" and "i+1" such that the resulting angles remain in structurally stable regions of Ramachandran space. The key requirement is that the "sum" of the ψ angle of residue "i" and the φ angle of residue "i+1" remain roughly constant; in effect, the flip is a crankshaft move