Looks are deceptive

Geometry Level 3

The circle α\alpha has center at (1,2)(1,2) and radius 33. The circle β\beta has center at (9,8)(9,8) and radius 77. They touch at the point (a,b)(a,b) where aa and bb are fractions with same denominator. Find the sum of their numerators and denominators (taken only once).

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