×

# Wild problem

In $$\Delta ABC$$ , let $$D,E,F$$ be mid points of $$BC \ , \ AC \ , \ AB$$ respectively and $$G$$ be the centroid. Then prove that for all points $$K$$ in the plane of triangle,

$\large AK^2+BK^2+CK^2+9GK^2=4(DK^2+EK^2+FK^2)$

Expecting numerous solutions.
Let's see who has the most elegant solution ;)

Note by Nihar Mahajan
1 year, 3 months ago

Sort by:

Well, there is a co-ordinate bash solution, but I don't think it is worth to type out the whole thing ( since the bash is trivial to do ). · 1 year, 1 month ago

I heard about you, you are SHINING STAR of our future . Please read out my 3rd note which is available on my PROFILE please read it out. I AM SURE IT WILL DEFINITELY help you to achieve your GOAL BEST OF LUCK.. · 1 year ago

Nihar Mahajan Sir; I have put a new topic as note on my profile. SCIENCE-a boon or bane PLEASE PUT YOUR POINT OF VIEWS ON THE DISCUSSION. · 1 year ago

The heart of the problem is use of $$apollonius ..theorem$$ over many times. · 1 year, 3 months ago