For a given quadrilateral A1A2B1B2, a point P is called phenomenal, if line segments A1A2 and B1B2 subtend the same angle at point P (i.e. triangles PA1A2 and PB1B2 which can be also also degenerate have equal inner angles at point P disregarding orientation).Three non-collinear points, A1,A2, and B1 are given in the plane. Prove that it is possible to find a disc in the plane such that for every point B2 on the disc, the quadrilateral A1A2B1B2 is convex and it is possible to construct seven distinct phenomenal points (with respect to A1A2B1B2) only using a right ruler.With a right ruler the following two operations are allowed:[*]Given two points it is possible to draw the straight line connecting them;
[*]Given a point and a straight line, it is possible to draw the straight line passing through the given point which is perpendicular to the given line.Proposed by Á. Bán-Szabó, Budapest komalgeometryconstruction