If $G$ be the centroid of a triangle $A B C$ and $O$ be any other point , then
$4 (G A^{2} + G B^{2} + G C^{2}) = B C^{2} + C A^{2} + A B^{2}$

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B False
This condition never be satisfied

As we know from the median properties
$A B^{2} + B C^{2} + A C^{2} = 3 (G A^{2} + G B^{2} + G C^{2})$

So given condition is false.

Suggest Corrections

Similar questions

3 (G A^{2} + G B^{2} + G C^{2}) = B C^{2} + C A^{2} + A B^{2}

O A^{2} + O B^{2} + O C^{2} = G A^{2} + G B^{2} + G C^{2}

A B^{2} + B C^{2} + C A^{2} = 3 (G A^{2} + G B^{2} + G C^{2}) .

P A^{2} + P B^{2} + P C^{2} = G A^{2} + G B^{2} + G C^{2} + 3 G P^{2}

G

A B C

P

P A^{2} + P B^{2} + P C^{2} = G A^{2} + G B^{2} + G C^{2} + 4 G P^{2}

G

△ A B C

\frac{A B^{2} + B C^{2} + C A^{2}}{A G^{2} + B G^{2} + C G^{2}}

Join BYJU'S Learning Program