Harvard MIT MT

Geometry Level 4

Let \(ABC\) be a triangle with \(AB = 5, AC = 4, BC = 6\). The angle bisector of \(C\) intersects side \(AB\) at \(X\). Points \(M\) and \(N\) are drawn on sides \(BC\) and \(AC\), respectively, such that \(\overline { XM } \parallel \overline { AC } \) and \(\overline { XN } \parallel \overline { BC } \). Compute the length \(MN\).

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