From a uniform circular disc a circular hole is cut out touching the rim of the disc at the poin...

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From a uniform circular disc a circular hole is cut out touching the rim of the disc at the point \( A \). Prove that the center of gravity \( G \) of the remainder is on the circumference of the hole if \( A G^{2}=A B \). \( G B \) where \( B \) is the other end of the diameter through \( A \) of the disc.
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