L and M are midpoints of equilateral triangle ABC, and LM meets the circumcircle of the triangle at Y. Prove LM/MY is the golden ratio.

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So far I've tried to split the triangle into smaller 30-60-90 triangles, and letting LM = x make some proportions and see if they can be related in anyway. I'm not sure what to do about MY though.

Any Ideas? Any and all help is appreciated.

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