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s \sqrt3 >= l_a + l_b + l_c, angle bisectors inequality

Source: IMAR Test 2003 p2

April 18, 2020
geometryangle bisectorgeometric inequalitysemiperimeter

Problem Statement

Prove that in a triangle the following inequality holds: s3≥ℓa+ℓb+ℓcs\sqrt3 \ge \ell_a + \ell_b + \ell_c where ℓa\ell_a is the length of the angle bisector from angle AA, and ss is the semiperimeter of the triangle
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