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In triangle ABC with centroid G, the median segment AG equals the side BC. Find the measure of angle BGC (in degrees).

1. 90 deg
2. 60 deg
3. 120 deg
4. 150 deg

Correct answer: 90 deg

Solution

Let M be the midpoint of BC. The condition AG = BC together with the centroid ratios forces GM (the median from G in triangle BGC) to equal half of BC, which is the well-known condition for a right angle at G.

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