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Problem 3

Part of 2003 Junior Macedonian Mathematical Olympiad

Problems(1)

Geometric inequality for radii of incircle and circumcircle

Source: 2003 Junior Macedonian Mathematical Olympiad P3

6/29/2021
Let ABCABC be a given triangle. The circumcircle of the triangle has radius RR, the incircle has radius rr, the longest side of the triangle is aa, while the shortest altitude is hh. Show that: Rr>ah\frac{R}{r} > \frac{a}{h}.
geometrygeometric inequalityinequalities