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The condition for two circles S  x2 + y2 + 2gx + 2fy + c = 0 and S' =  x2 + y2 + 2ga(x) + 2f'y + c' = 0 to cut orthogonally is that 2gg' + 2ff' + c + c'.

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The two circles cut each other orthogonally

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