Three medians of triangle ABC intersect at a point G. Is triangle ABC

Question

Three medians of triangle ABC intersect at a point G. Is triangle ABC scalene?

(1) GA = GB

(2) GB = GC

Tulkin987 · Answer

First pay attention to this property of median:  the centroid divides each median into parts in the ratio  2:1 , with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex.

So, point  G  is the centroid.

(1) If  GA=GB , according to the above property, medians with vertice  A  and  B  are equal. We have equilateral triangle. Answer is NO.  Sufficient.

(2) The same is true. Medians with vertice  B  and  C  are equal, and we have equilateral triangle. Answer is NO.  Sufficient.

Answer: D

amanvermagmat · Answer

Hello

Yes I agree that answer would be D. But may I point out that from first statement, GA=GB means that medians from A and B are equal, which tells us that triangle is isosceles. Not necessarily equilateral. Same from statement 2 also.

Of course still this information is sufficient to say NO to the question asked, and hence answer should be D.

Tulkin987 · Answer

Yes, you are right!

Three medians of triangle ABC intersect at a point G. Is triangle ABC

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