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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]? 

 

\

 

Thanks in advance for whoever helps! :)

 Nov 16, 2020
edited by iamhappy  Nov 16, 2020
 #1
avatar+112011 
+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.

 

 Nov 16, 2020
 #2
avatar+413 
+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
 #3
avatar+112011 
+1

Tiggsy has given some brilliant answers here. 

I am very glad that you found this one   cool

 

Thanks Tiggsy and thanks Iamhappy.       cool laugh cool

Melody  Nov 18, 2020
 #4
avatar+112011 
+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

 Nov 20, 2020

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