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Sine inequality greater than twice triangle area

Source: AIMO 2007, TST 5, P3

January 11, 2009
trigonometryinequalitiesgeometrysearchgeometry unsolved

Problem Statement

Let ABC ABC be a triangle and P P an arbitrary point in the plane. Let α,β,γ \alpha, \beta, \gamma be interior angles of the triangle and its area is denoted by F. F. Prove: \ov{AP}^2 \cdot \sin 2\alpha + \ov{BP}^2 \cdot \sin 2\beta + \ov{CP}^2 \cdot \sin 2\gamma \geq 2F When does equality occur?
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