Looks are deceptive
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).
In case you'd like to know the source of this question, let me tell you that this question trolled 1.5 lakh students in TN NTSE -2014