WEISS Gunter3D-Versions of Theorems related to Miquel´s TheoremThe elementary geometric Miquel theorem concerns a triangle ABC and points R,S,T on its sides, and it states that the circles ART, BRT, CST have a common point M, the Miquel point to these givens. For M there exists a two-parametric set of possibilities, such that there exists a one-parameter set of point triplets R,S,T to a given point M. Choosing R,S,T in special ways one receives the so-called “Beermat theorem”, the Brocard theorems, and the Simson-Wallace theorem as special cases of Miquel´s theorem. Remaining within Euclidean geometry we deal with 3D modifications of these theorems. |