KVPY sample question

JEE Main 2015 Questions › Co-ordinate Geometry questions › KVPY sample question

Let P be an interior point of a triangle ABC. Extend AP, BP, CP to meet BC, CA,
AB respectively in D, E, F. Suppose the areas of the triangles APE, APF and BPD are equal,
prove that P is the centroid of triangle ABC.

#Mathematics #Co-ordinate Geometry

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5 Answers

Gurtej Singh ·2010-10-20 21:04:43

Hey...... Anybody pls answer..... 5 marks question...

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jeetopper jee ·2010-10-21 23:05:53

I think its easy since if the given triangles have equal areas they must be congruent n now simple reasoning show that d e f are mid pts thus making p as centroid.

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Abhisek ·2010-10-22 00:16:04

@ jeetopper : Can u plz prove that the given trianlges are congruent ? Congruent triangles have equal areas but the reverse MAY NOT be true always...