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Geometrical problem

solakis

Active member
Dec 9, 2012
304
Given a triangle ABC and a point M inside the triangle ,draw perpendiculars MZ,MD,ME at the sides AB,BC,AC respectively. Then prove:


\(\displaystyle \frac{AB}{MZ}+\frac{AC}{ME}+\frac{BC}{MD}\geq\frac{2t}{r}\)

Where t is half the perimeter of the triangle and r is the radius of the inscribed circle
 

solakis

Active member
Dec 9, 2012
304
Here also the Cauchy-Schwarz inequality may be used for the solution of the problem