MathDB

1

Part of 2001 South africa National Olympiad

Problems(1)

p/2 < AC + BD < p

Source: South Africa 2001

10/1/2005
ABCDABCD is a convex quadrilateral with perimeter pp. Prove that 12p<AC+BD<p. \dfrac{1}{2}p < AC + BD < p. (A polygon is convex if all of its interior angles are less than 180∘180^\circ.)
geometryperimeterinequalitiestriangle inequality