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# Geo

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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]?

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Thanks in advance for whoever helps! :)

Nov 16, 2020
edited by iamhappy  Nov 16, 2020

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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
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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
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Tiggsy has given some brilliant answers here.

I am very glad that you found this one

Thanks Tiggsy and thanks Iamhappy.

Melody  Nov 18, 2020
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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