Triangle Geometry: Prove AO/AD+BO/BE+CO/CF=2

[thereddevils]

Homework Statement

O is any point inside the triangle ABC. AO, BO, CO are joined and produced to meet the opposite sides BC, CA, and AB at D,E and F respectively. Prove that AO/AD+BO/BE+CO/CF=2

Homework Equations

The Attempt at a Solution

Obviously, O is meant to be the centroid. The question did not say that the lines produced cut the opposite sides into two equal lengths, where D,E and F are midpoints of the respective sides they cut. Shouldn't the question include this piece of information?

 

[Coto]

O is explicitly stated to be any point in the triangle, is there any reason you restricted it to be a single point in the triangle?

 

[thereddevils]

O is explicitly stated to be any point in the triangle, is there any reason you restricted it to be a single point in the triangle?

Thanks Coto, that's a misinterpretation by me. I will attempt to solve this using the ceva's theorem.