Source (Romanian Math Magazine - Gazeta Matematica; online competition)
Trying the drawing in Geogebra, I found the angle is 30 degrees, regardless of value of angle C (moving B on the bisector OB). Is there some theorem which I could use to derive this?
From the figure, BDO = 90 - BCD (also don't know how to prove it).
I am interested in a solution for elementary school students.