MathDB

For a given quadrilateral

A_1A_2B_1B_2,

a point

P

is called phenomenal, if line segments

A_1A_2

and

B_1B_2

subtend the same angle at point

P

(i.e. triangles

PA_1A_2

and

PB_1B_2

which can be also also degenerate have equal inner angles at point

P

disregarding orientation).
Three non-collinear points,

A_1,A_2,

and

B_1

are given in the plane. Prove that it is possible to find a disc in the plane such that for every point

B_2

on the disc, the quadrilateral

A_1A_2B_1B_2

is convex and it is possible to construct seven distinct phenomenal points (with respect to

A_1A_2B_1B_2

) 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

Problem Statement