Miquel Equation

$$\dirang A_2MA_3 =\dirang A_2A_1A_3+\dirang P_2P_1P_3,$$

where $\dirang$ is a Directed Angle.

See also Directed Angle, Miquel's Theorem

References

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 131-144, 1929.