A circle touches the line \( y=x \) at a point \( P \) such that \( O P=4 \sqrt{2} \), where \( ...

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A circle touches the line \( y=x \) at a point \( P \) such that \( O P=4 \sqrt{2} \), where \( O \) is the origin. The circle contains the point \( (-10,2) \) in its interior and the length of its chord on the line \( x+y=0 \) is \( 6 \sqrt{2} \). Determine the equation of the circle.
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