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AD, BE and CF are the medians of triangl...

AD, BE and CF are the medians of triangle ABC whose centroid is G. If the points A, F, G and E are concyclic, then prove that `2a^(2) = b^(2) + c^(2)`

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To prove that \(2a^2 = b^2 + c^2\) given that points A, F, G, and E are concyclic in triangle ABC with medians AD, BE, and CF, we can follow these steps: ### Step-by-Step Solution 1. **Understanding the Triangle and Medians**: - Let triangle ABC have vertices A, B, and C. - Let D, E, and F be the midpoints of sides BC, AC, and AB respectively. - The medians AD, BE, and CF intersect at the centroid G. ...
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