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OlympiadSuperchallengeOlympiad Number Theory

Olympiad Number Theory · Superchallenge problem

In triangle ABCABC with side lengths a=7a = 7, b=8b = 8, c=9c = 9, the incenter has barycentric coordinates (a:b:c)(a : b : c). Compute the normalized coordinate of the incenter with respect to vertex AA (the ratio [IBC]/[ABC][IBC]/[ABC]). Express your answer as a common fraction.