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P interior of ABC, BP > AP and BP > CP => <ABC< 90^o

Source: Ukrainian Geometry Olympiad 2020, VIII p2 , IX p1

April 27, 2020
anglesacutegeometry

Problem Statement

Inside the triangle ABCABC is point PP, such that BP>APBP > AP and BP>CPBP > CP. Prove that ∠ABC\angle ABC is acute.
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