The symbol ∡A B C denotes the directed angle from A B to B C, which is the signed angle through which A B must be rotated about B to coincide with B C. Four points A B C D lie on a circle (i.e., are concyclic) iff ∡A B C = ∡A D C. It is also true that ∡l_1 l_2 + ∡l_2 l_1 = 0° or 360°. Three points A, B, and C are collinear iff ∡A B C = 0° or 180°. For any four points, A, B, C, and D, ∡A B C + ∡C D A = ∡B A D + ∡D C B.

angle | collinear | concyclic | Miquel equation