Let Γ be a circle with center O. Let AC be a chord
of Γ (not containing O).
be a point on chord AC (not A or C). The line through D and perpendicular to AC
intersects Γ in points B1 and B2. Let H1 and H2
be the orthocenters of triangles
AB1C and AB2C respectively.
Define the point of intersection of the bisectors of angles H1B1O and
prove your result.