when reflections of vertices cyclic ABCD wrt diagonals are collinear/ concyclic
Source: 2021 Austrian Federal Competition For Advanced Students, Part 2, p5
June 6, 2021
geometryreflectioncyclic quadrilateralConcycliccollinear
Problem Statement
Let be a convex cyclic quadrilateral with diagonals and . Each of the four vertixes are reflected across the diagonal on which the do not lie.
(a) Investigate when the four points thus obtained lie on a straight line and give as simple an equivalent condition as possible to the cyclic quadrilateral for it.
(b) Show that in all other cases the four points thus obtained lie on one circle.(Theresia Eisenkölbl)