In the plane, three distinct non-collinear points A,B,C are marked. In each step, Ege can do one of the following:
[*] For marked points X,Y, mark the reflection of X across Y.[*]For distinct marked points X,Y,Z,T which do not form a parallelogram, mark the center of spiral similarity which takes segment XY to ZT.[*] For distinct marked points X,Y,Z,T, mark the intersection of lines XY and ZT.
No matter how the points A,B,C are marked in the beginning, can Ege always mark, after finitely many moves,a) The circumcenter of △ABC.b) The incenter of △ABC.Proposed by Deniz Can Karaçelebi
geometrycomplex numbersSpiral Similarity