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perimeter of ABC>2 OC, C in <AOB =90^o (2021 Kyiv City MO Round2 7.4.1)

Source:

February 16, 2021
geometryperimetergeometric inequalityright angle

Problem Statement

Point CC lies inside the right angle AOBAOB. Prove that the perimeter of triangle ABCABC is greater than 2OC2 OC.