IMO Shortlist 1989 problem 32
Dodao/la:
arhiva2. travnja 2012. The vertex
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
of the acute triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
is equidistant from the circumcenter
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
and the orthocenter
![H.](/media/m/c/8/8/c889c44af9e2839727c30e46ac5c3665.png)
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