The measure of the chord intercepted by circle $x^2+y^2=9$ and the line $x-y+2=0$ is.

We use the half-chord length formula, L = sqrt(r^2 - p^2), where r is the radius and p is the perpendicular distance from the center to the line. The circle x^2+y^2=9 has center (0,0) and radius r=3. The perpendicular distance from (0,0) to the line x-y+2=0 is p = |0-0+2| / sqrt(1^2 + (-1)^2) = 2/sqrt(2) = sqrt(2). The half-chord length is sqrt(3^2 - (sqrt(2))^2) = sqrt(9-2) = sqrt(7). The full length of the chord is twice the half-chord length, which is 2*sqrt(7) = sqrt(28). The result is sqrt(28).

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