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If a + b + c = 2s then ((s - a)^(2) ...

If ` a + b + c = 2s` then
`((s - a)^(2) + (s - b)^(2) +(s - c)^(2) +s^(2))/(a^(2) + b^(2) + c^(2))` is equal to

A

`a^2 +b^2+c^2`

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`((s-a)^2 + (s-b)^2 +(s-c)^2 +s^2)/(a^2+b^2+c^2)`
`=((S^2-2as+a^2)+(S^2-b^2-2bs)(S^2+c^2-2sc)+S^2)/(a^2+b^2+c^2)`
`=(4S^2+a^2+b^2+c^2-2s(a+b+c))/(a^2+b^2+c^2)`
`=(4S^2+a^2+b^2+c^2-2s(2S))/(a^2+b^2+c^2)`
`=(a^2+b^2+c^2)/(a^2+b^2+c^2)=1`
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