CZ-SK-MO 1983 Problem 2

Given a triangle $ABC$ , prove that for every inner point $P$ of the side $AB$ the inequality $PC\cdot AB<PA\cdot BC+PB\cdot AC$ holds.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.