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Please give a detailed proof of this question! 3. Recall that the Gergonne point of a...

Please give a detailed proof of this question!

3. Recall that the Gergonne point of a triangle is the point of concurrency of the three Cevians formed by joining the vertices of the triangle to the points of tangency of the incircle opposite each vertex. Let T be the Gergonne point of Triangle ABC. Show that if T coincides with the circumcenter or the orthocenter or the centroid of Triangle ABC, then the triangle must be equilateral.

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