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Show that R / r > a / h in any triangle ABC

Source: Tournament of Towns Spring 2003 - Junior A-Level - Problem 2

June 14, 2011
trigonometryinequalitiesgeometrycircumcircletriangle inequalitygeometry unsolved

Problem Statement

Triangle ABCABC is given. Prove that Rr>ah\frac{R}{r} > \frac{a}{h}, where RR is the radius of the circumscribed circle, rr is the radius of the inscribed circle, aa is the length of the longest side, hh is the length of the shortest altitude.