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Geometry Level 3

The circle \(\alpha\) has center at \((1,2)\) and radius \(3\). The circle \(\beta\) has center at \((9,8)\) and radius \(7\). They touch at the point \((a,b)\) where \(a\) and \(b\) are fractions with same denominator. Find the sum of their numerators and denominators (taken only once).

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