Harvard MIT MT

Geometry Level 4

Let ABCABC be a triangle with AB=5,AC=4,BC=6AB = 5, AC = 4, BC = 6. The angle bisector of CC intersects side ABAB at XX. Points MM and NN are drawn on sides BCBC and ACAC, respectively, such that XMAC\overline { XM } \parallel \overline { AC } and XNBC\overline { XN } \parallel \overline { BC } . Compute the length MNMN.

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