Miquel point and isogonal conjugation

Abstract

We study the possible positions of the Miquel point in the plane of a given triangle, which Miquel triangles are similar to the given one. We found out that these positions are eleven. We also study the possible positions of the Miquel point in the plane of a given triangle, where among the families of Miquel triangles there are triangles, which are similar to the given triangle. We study which of them are isogonal conjugated.