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Part of 1932 Eotvos Mathematical Competition

Problems(1)

< FAP < < PAT if ABC is acute triangle.

Source: Eotvos 1932 p2

9/10/2024
In triangle ABCABC, AB≠ACAB \ne AC. Let AFAF, APAP and ATAT be the median, angle bisector and altitude from vertex AA, with F,PF, P and TT on BGBG or its extension. (a) Prove that PP always lies betweenF F and TT. (b) Prove that ∠FAP<∠PAT\angle FAP < \angle PAT if ABCABC is an acute triangle.
Geometric Inequalitiesgeometry