1985 AIME Problems/Problem 9

Problem

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

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