In a circle, parallel chords of lengths 2,3,4 determine central angles $$\alpha ,\beta ,\alpha +\beta$$ radians, respectively, where $$\alpha +\beta <\pi$$, If $$\cos \alpha$$, Which is a positive rational numbers, is expressed as a fraction in lowest terms, what is the sum of its numerator and denominator?

(第三届AIME1985 第9题)