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angle inequality involving centroid of triangle

Source: Serbia & Montenegro TST 2005 problem 4

June 1, 2005
inequalitiestrigonometrygeometry proposedgeometry

Problem Statement

Let TT be the centroid of triangle ABCABC. Prove that 1sin⁡∠TAC+1sin⁡∠TBC≥4 \frac 1{\sin \angle TAC} + \frac 1{\sin \angle TBC} \geq 4
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