Anele Clive Moli's Method: Constructing an equilateral triangle

In August 2012, when I asked my class of prospective mathematics teachers to construct a 'dynamic equilateral triangle' themselves, Anele Moli, a student, came up with the novel construction below. Click on the buttons in Steps 2 and 3 below.

Please install Java (version 1.4 or later) to use JavaSketchpad applets.

Anele's Method: Constructing an equilateral triangle

Drag A or B to check if it remains equilateral. Can you explain (prove) why his method works? If stuck, try this Hint.

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Michael de Villiers, 30 August 2012.