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...--prophetes.ai

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 $OC = OD$. Image1 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.

As you can see from the picture, your claim is not true. You need some other hypotheses.

![enter image description here](