The sum of the square of the length of the chords intercepted by the line $x + y = n, n \in N$ on the circle $x^{2} + y^{2} = 4$

5

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11

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22

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25

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Solution

The correct option is A $22$
${A B}^{2} = 4 {A M}^{2} = 4 (4 - \frac{n^{2}}{2}) = 2 (8 - n^{2})$
Hence, required sum $= 2 (8 - 1^{2} + 8 - 2^{2}) = 2 \times 11 = 22$

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