Triangle Inequality Proof Using Euclidean Geometry

[ilaneden]

proof the following using only euclidean geometry:
Let S be any point inside a triangle ABC and let SP; SQ; SR be
perpendicular to the sides BC;CA;AB respectively, then
SA + SB + SC >= 2 (SP + SQ + SR)
Hint: Set P1; P2 be the feet of the perpendiculars from R and Q upon
BC. Prove first that (i) QR >= P1P2 and (ii) PRP1 and SBR are
similar triangles.

 

[Eynstone]

This is a standard inequality , named after Erdo:s.