# Looks are deceptive

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).

Note

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

×