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Found problems: 1

2014 AIME Problems, 12
Suppose that the angles of $\triangle ABC$ satisfy $\cos(3A) + \cos(3B) + \cos(3C) = 1$. Two sides of the triangle have lengths $10$ and $13$. There is a positive integer $m$ so that the maximum possible length for the remaining side of $\triangle ABC$ is $\sqrt{m}$. Find $m$.
trigonometry trig identities tangent half angle casework geometry law of cosines number theory trigonometric identities