MathDB
Parallel chords

Source:

March 14, 2006
trigonometryrotationAMCAIMEtrig identitiesLaw of Cosines

Problem Statement

In a circle, parallel chords of lengths 2, 3, and 4 determine central angles of α\alpha, β\beta, and α+β\alpha + \beta radians, respectively, where α+β<π\alpha + \beta < \pi. If cos⁡α\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?
Back to ProblemsView on AoPS