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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 $OC = OD$.

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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?
I'm sorry for bad English.
Thanks.

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    $\begingroup$ The statement is not true if there is no restriction to the point $B$. Do you mean $B$ is the midpoint of that semicircle? $\endgroup$ – Cave Johnson Jul 30 '16 at 10:56
  • $\begingroup$ B is on semicircle But we don't know where is it. if we draw it then B is the midpoint of that semicircle but we don't know it. $\endgroup$ – Amin Jul 30 '16 at 11:00
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As you can see from the picture, your claim is not true. You need some other hypotheses.

enter image description here

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  • $\begingroup$ thanks. It's not my question But I believe that it's question is not true. $\endgroup$ – Amin Jul 30 '16 at 12:06

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