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Area of triangle

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Consider the following statements : 1. Let D be a point on the side BC of a triangle ABC: If area of triangle ABD = area of triangle ACD, then for all points O on AD, area of triangle ABO = area of triangle ACO. 2. If G is the point of concurrence of the medians of a triangle ABC, then area of triangle ABG = area of triangle BCO = area of triangle ACG. Which of the above statements is/are correct?

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