3

Part of 1985 Brazil National Olympiad

Problems(1)

inequality with perimeter and sum of diagonals of inscribed quadrilateral

Source: Brazilian Mathematical Olympiad 1985 P3

A convex quadrilateral is inscribed in a circle of radius

1

. Show that the its perimeter less the sum of its two diagonals lies between

0

2

inequalitiesgeometryperimetercyclic quadrilateral