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Let G be the centroid of the DeltaABC, w...

Let G be the centroid of the `DeltaABC`, whose sides are of lengths a,b,c. If P be a point in the plane of `triangleABC`, such that `PA=1,PB=3, PC=4` and `PG=2`, then the value of `a^(2)+b^(2)+c^(2)` is

A

42

B

40

C

36

D

28

Text Solution

Verified by Experts

The correct Answer is:
A
As `|veca+vecb+vecc|^(2)+ |veca-vecb|^(2)+|vecb-vecc|^(2)+|vecc-veca|^(2)`
`=3(|veca|^(2)+|vecb|^(2)+|vecc|^(2))`
So, `9(GP)^(2)+(AB)^(2)+(BC)^(2)+(CA)^(2)`
`=3(PA)^(2)+(PB)^(2)+(PC)^(2)`
`rArr 9 xx 2^(2)(a^(2)+b^(2)+c^(2))=3(1^(2)+3^(2)+4^(2))`
`rArr a^(2)+b^(2)+c^(2)=42`
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