In an equilateral triangle show that the incentre, the circumcentre, the orthocenter and the centroid are the same point.
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Their point of concurrency is O, which is the centroid of the triangle. TO PROVE THAT: Centroid O is the circumcentre of the triangle ABC. If we prove that centroid O is the circumcentre of the triangle, then it automatically becomes the centre of the circumcircle. PROOF: Since AP is median, so P is mid point of BC.
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