# Equilateral triangle in Semicircular

I have a geometry question. In this question, We have a Equilateral triangle ($\triangle BDC$) that we draw it with one point on the circle and 2 point on the diameter. We want to prove if we draw this triangle then $OC = OD$.

I try to prove it But I can't find any good way to prove that. It must solve with central and inscribed angles. Is it possible to help me to solve it?
• The statement is not true if there is no restriction to the point $B$. Do you mean $B$ is the midpoint of that semicircle? – Cave Johnson Jul 30 '16 at 10:56