An interesting problem in Geometry

In , a line passing through the centroid of the triangle intersects with segments and at and respectively .

Show that :

Quote:

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Originally Posted by simplependulum

In , a line passing through the centroid of the triangle intersects with segments and at and respectively .

Show that :

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Dear simplependulum,

Thanks for submitting this question. I tried it for several days and finally came up with an answer.

Thanks for the reply , I worried that no one may feel interested in this problem which seems an easy task but actually it needs some time to finish .

Excellent ! You utilized Menelaus Theorem to solve this problem . I think Menelaus and Ceva is one of the greatest stone in pure geometry , they are applicable and powerful indeed !