The segments AB and DC lie on parallel lines, and the segments AC and BD intersect at point M. Find MC if AB = 16, DC = 24, AC = 25.

Consider the triangles ABM and CDM.
∠AMB = ∠CMD (as they are vertical).
∠ABM = ∠CDM (because they are cross-lying).
Therefore, the triangles ABM and CDM are similar (by the first sign of similarity).
AC = AM + MC => AM = AC-MC
Then:
AB / CD = AM / MC
16/24 = (AC-MC) / MC
16MC = 24 (25-MC)
2MC = 3 (25-MC)
2MC = 75-3MC
5MC = 75
MC = 15
Answer: MC = 15

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