BE, CF are two medians of $$\triangle $$ABC and G is their point of intersection. EF cuts AG at O. Ratio of AO : OG is equal to

BE, CF are two medians of $$\triangle $$ABC and G is their point of intersection

$$=$$>  AB = 2AF  and   AC = 2AE

$$=$$>  G is the centroid of the $$\triangle $$ABC and divides the median AH in the ratio 2 : 1

$$=$$>  AG : GH = 2 : 1

$$=$$>  AG = 2GH ...................(1)

$$\triangle $$AFE  is similar to $$\triangle $$ABC

$$=$$>  $$\frac{AF}{AB}=\frac{AO}{AH}$$

$$=$$>  $$\frac{AF}{2AF}=\frac{AO}{AG+GH}$$

$$=$$>  $$\frac{1}{2}=\frac{AO}{2GH+GH}$$

$$=$$>  $$\frac{1}{2}=\frac{AO}{3GH}$$

$$=$$>  GH = $$\frac{2}{3}$$AO .................(2)

From (1) and (2)

AG = 2($$\frac{2}{3}$$AO)

$$=$$>  AO + OG = $$\frac{4}{3}$$AO

$$=$$>  OG = $$\frac{4}{3}$$AO - AO

$$=$$>  OG = $$\frac{1}{3}$$AO

$$=$$>  $$\frac{AO}{OG}=\frac{3}{1}$$

$$=$$>  AO : OG = 3 : 1

Hence, the correct answer is Option A