hi, I am a little stuck on this question. It's pretty hard (for me at least) so, i hope you can help!

G is the centroid of triangle ABC. G_1,G_2, and G_3 are the centroids of triangle BCG, triangle CAG, and triangle ABG respectively. What is [G_1G_2G_3] / [ABC]?

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Thanks in advance for whoever helps! :)

iamhappy Nov 16, 2020

#1**+2 **

I am more than a little stuck myself.

I have drawn the pic. I hope the link works properly (let me know)

https://www.geogebra.org/classic/fhkhhxuf

**You can drag the points around to make any triangle you want.**

It is visually clear that the 2 triangles are similar.

The second is reduced about the point G and is then reflected

This can clearly be seen in the pic below.

Melody Nov 16, 2020

#2**+2 **

Hi Melody!

thank you so much for your response!

the link does work (thankfully) and I tried to play around, but I was still stuck.

However, I seemed to find this, https://web2.0calc.com/questions/triangle-medians-and-altitudes#r7

tiggsy explained pretty well, and after reading it a few times I understood pretty much.

I pretty much saw that the ratio would be 1/6

To tiggsy and melody, thank you!

Have a wonderful day!

iamhappy
Nov 18, 2020

#4**+1 **

I have looked at Tiggsy's solution and I have a query.

If anyone knowledgeable wants to answer me that would be good.

https://web2.0calc.com/questions/triangle-medians-and-altitudes#r11

Melody Nov 20, 2020