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hinged equilateral triangles and circumcircles

Author:
Arthur Lee
Topic:
Equilateral Triangles, Triangles
Two equilateral triangles share a vertex A. Their circumcircles meet at A and another point F. Are the points C, D, F collinear? How about B, E, F? Drag the free points to see whether their relations change or not. Can you explain the observed relations?

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