If G is the centroid of (\triangle ABC) and (AG = BC), then find the (\angle BGC).

In any triangle, AG:GD = 2:1 where D is the midpoint of BC. If AG = BC, let BC = 3 units, so AG = 3 and GD = 1.5. In triangle BGD, BG is a median. Using the fact that AG = BC creates an isosceles condition. More directly, when AG = BC in a right triangle context, angle BGC = 90°. This follows from the property that if the centroid divides the median in 2:1 ratio and AG equals BC, the triangle must be right-angled at A.