Let C be a circunference, O is your circumcenter, AB is your diameter and R is any point in C (R is different of A and B)
Let P be the foot of perpendicular by O to AR, in the line OP we match a point Q, where QP is 2OP and the point Q isn't in the segment OP.
In Q, we will do a parallel line to AB that cut the line AR in T.
Denote H the point of intersections of the line AQ and OT.
Show that H, B and R are collinears. geometrygeometry unsolvedcono sur