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(A) The equation of the circle is $x^2 + y^2 = 25$,which has center $C(0, 0)$ and radius $r = 5$.The line passes through $P(-\sqrt{8}, \sqrt{8})$ with

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$10$

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(A) The equation of the circle is $x^2 + y^2 = 25$,which has center $C(0, 0)$ and radius $r = 5$.The line passes through $P(-\sqrt{8}, \sqrt{8})$ with slope $m = 	an(135^{\circ}) = -1$.The equation of the line is $y - \sqrt{8} = -1(x + \sqrt{8})$,which simplifies to $x + y = 0$.The perpendicular distance $d$ from the center $(0, 0)$ to the line $x + y = 0$ is $d = \frac{|0 + 0|}{\sqrt{1^2 + 1^2}} = 0$.Since the distance $d = 0$,the line passes through the center of the circle.Therefore,the chord $AB$ is a diameter of the circle.The length of the diameter is $2r = 2 	imes 5 = 10$.

If a line passing through the point $\left( -\sqrt{8}, \sqrt{8} \right)$ and making an angle of $135^{\circ}$ with the $x$-axis intersects the circle $x = 5 \cos \theta, y = 5 \sin \theta$ at points $A$ and $B$,then find the length of the chord $AB$.

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