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

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

1:1

2:1

3:1

3:2

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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:-