In the given figure, BC is the diameter of the circle. AB is a tangent

angle BDC = angle ABC = 90*

angle C is common in both triangles

Using AA criterion, we can say that both triangles are similar.

If this weren't a GMAT question (so we had no answer choices, or needed to prove why the answer is what it is), I'd solve the way nick did above, but if it is a GMAT question, we can solve without doing much work:

If this question has just one answer, then the answer must be the same no matter where point D is. If the answer changed when we moved point D around, one of the answer choices would need to be "cannot be determined". So we can freely put point D anywhere we like. If we put point D so it is millimeters away from point B (so the length of line AB is almost zero), then AC and DC will both almost be identical to the diameter of the circle, and will both therefore be almost exactly 8 units long. So their product will be extremely close (or equal) to 64, and that's the only plausible answer choice.

Need to clarify how sides are in ratio….how it is been assumed that sides AB = BC

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WE CAN CONSIDER OTHER TRIANGLES AS SIMILAR TO GET THE SOLUTION. HAVE A LOOK AT THE PICTURE.