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Inequality for the incircle

Source: French TST 2004, pb. 5; 16th KMO #4

May 25, 2004
inequalitiesgeometryincentertrigonometryinradiusperimetercyclic quadrilateral

Problem Statement

Let PP, QQ, and RR be the points where the incircle of a triangle ABCABC touches the sides ABAB, BCBC, and CACA, respectively. Prove the inequality BCPQ+CAQR+ABRP≥6\frac{BC} {PQ} + \frac{CA} {QR} + \frac{AB} {RP} \geq 6.
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