Geometry (congruent triangle mcq)

lokamo said:
Dear All, How to solve this mcq pls? thinking.............
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First, the problem is incorrect; they don't say what triangle ABC is congruent to! I suspect they meant to say it is an equilateral triangle, since that is what it looks like (and that makes it possible to answer).

Second, if you've seen how this site works, you should know that we want you to show your own thinking first, so we know how to help you. Please do so. (I'd suggest looking for similar or congruent triangles, and labeling angles.)

(There's also a shortcut, if you don't mind cheating on the math: If the answer is one of the choices, then it is a constant regardless of the location of D, so you could just pick a convenient location ...)
 
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