Let $ABC$ be an equilateral triangle with centre $O$. A line through $C$ meets the circumcircle of triangle $AOB$ at points $D$ and $E$. Prove that points $A, O$ and the midpoints of segments $BD, BE$ are concyclic.
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Tags: geometry, Equilateral, circumcircle, Concyclic
Let $ABC$ be an equilateral triangle with centre $O$. A line through $C$ meets the circumcircle of triangle $AOB$ at points $D$ and $E$. Prove that points $A, O$ and the midpoints of segments $BD, BE$ are concyclic.