Can you do this without trigonometry?

Geometry Level 4

A circle, centre OO, has ABAB as a diameter. Let CC be a point on the circle different from AA and BB, DD be the point on ABAB such that CDB=90\angle CDB = 90^{\circ} and MM be the point on BCBC such that BMO=90\angle BMO = 90^{\circ}. If DBDB is 3×OM3 \times OM, calculate ABC\angle ABC in degrees.

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