Locus of the middle points of the line s...

Locus of the middle points of the line segment joining `P(0, sqrt(1-t^2) + t) and Q(2t, sqrt(1-t^2) - t)` cuts an intercept of length `a` on the line `x+y=1`, then `a =` (A) `1/sqrt(2)` (B) `sqrt(2)` (C) `2` (D) none of these

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