The vertex of the acute triangle is equidistant from the circumcenter and the orthocenter Determine all possible values for the measure of angle
%V0
The vertex $A$ of the acute triangle $ABC$ is equidistant from the circumcenter $O$ and the orthocenter $H.$ Determine all possible values for the measure of angle $A.$
Izvor: Međunarodna matematička olimpijada, shortlist 1989
Školjka 
of the acute triangle 
is equidistant from the circumcenter 
and the orthocenter 
Determine all possible values for the measure of angle 