In any triangle, the centroid divides the median in the ratio of:

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1:1

2:1

3:1

3:2

answer is B.

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Detailed Solution

Let us first of all draw the triangle named as ABC with its medians and centroid.
seo

Now we will extend AD to K such that AG = GK as well as join BK and CK.
We will then get a figure looking as follows:-
seo

Now look at △ABK
Since, F and G are midpoints of AB and AK respectively (Because we extended AB such that AG = GK).
∴ FG || BK (By the mid – point theorem)
Now since FG is a part of FC, therefore we will get:-
∴ GC || BK …………………(1)
Now look at △ACK
Since, E and G are midpoints of AC and AK respectively (Because we extended AB such that AG = GK).
∴ GE || CK (By the mid – point theorem)
Now since GE is a part of BE, therefore we will get:-
∴ BG || CK …………………(2)
Now using (1) and (2), we get that:-
BGCK is a parallelogram.
We know that diagonals in a parallelogram bisect each other.
∴ GD = DK ……………….(3)
And we already have AG = GK
We can write it as follows:-
⇒ AG = GD + DK
Now, on using (3), we will get the following expression:-
⇒ AG = 2GD
Now, we can write this as following expression:-

\Rightarrow \frac{AG}{GD} = \frac{2}{1}

∴ the centroid of the triangle divides each of its median in the ratio 2:1.
Hence, the correct option is (2).

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