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The Unity Pieces Theorem

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Prove that no two cevians drawn inside a triangle bisect each other.

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In the adjoining figure, the lines LQ, YP and XM have been drawn parallel to the sides AB, BC and AC respectively through the point ‘O’ lying inside ΔABC. If the areas of Δ OXY , Δ OLM and Δ OPQ are a

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