Assuming M is the intersection of MN with AB, and N is the intersection of MN and AC:
Angle ACP = angle BCP (by definition)
Angle NCP = angle BCP (intersection of line with parallel lines produces equal angles)
Triangle CPN is isoceles (two equal angles), and line NP = CN
Same argument for line MP = BM
Therefore NP + MP (i.e, MN) = CN + BM
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