Sum of the square of the length of the c...

Sum of the square of the length of the chord intersected by the line `x+ y =n , n in N` on circle `x^2+y^2=4` is: (A) 11 (B) 22 (C) 33 (D) none of these

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`x^2+(n-x)^2=4`
`2x^2-2nx+n^2-4=0`
`x_1+x_2=n`
`x_1x_2=(n^2-4)/2`
similarly,
`y_1+y_2=n`
`y_1y_2=(n-x_1)(n-x_2)`
`=(n^2-4)/2`
...

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