Pointer 1

Geometry Level 2

In a △ A B C \triangle ABC there is a point P P such that Area of △ A B P \triangle ABP = Area of △ A C P \triangle ACP = Area of △ B C P \triangle BCP , then P P is

Orthocentre Incentre Circumcentre Centroid

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Rajen Kapur by Rajen Kapur , 72, India

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1 solution

Blcraft Gaming
Feb 22, 2018

One special property of a triangle is that when you draw all the medians of a triangle, the areas of each of the little triangles formed are equal. (You can see this in action by balancing a triangle on its centroid.) The name of the point where the medians concur is the centroid. Therefore, the answer to the problem is the centroid.

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