2015 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 3
Show that the bisect of an angle in a triangle divides the opposite side in segments whose lengths have the same ratio as the ratio of the adjacent sides, in the picture below. NOTE: The same is true for the bisector of an exterior angle of a triangle, i.e., it divides the opposite side externally into segments that are proportional to the adjacent sides. You do not have to write a proof of this fact.
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