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368

Part of 1983 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 368 All Soviet Union MO 1983 maximal sidelength inequality

Source:

7/28/2019
The points D,E,FD,E,F belong to the sides (AB),(BC)(AB), (BC) and (CA)(CA) of the triangle ABCABC respectively (but they are not vertices). Let us denote with d0,d1,d2d_0, d_1, d_2, and d3d_3 the maximal side length of the triangles DEFDEF, DEADEA, DBFDBF, CEFCEF, respectively. Prove that d0≥32min{d1,d2,d3}d_0 \ge \frac{\sqrt3}{2} min\{d_1, d_2, d_3\} When the equality takes place?
geometric inequalityinequalitiesgeometry