Hello ordinalhighI think that the question can be re-written like this:

is any point in the interior of a triangle . Transversals , and are produced to meet the opposite sides at points , and respectively. Prove that:The reason I think this is correct is that when is the centroid of the triangle, each of the ratios is equal to , and the sum is therefore .

I think that you might be able to prove it using Ceva's Theorem, but so far I'm afraid I've drawn a blank.

Grandad