MathDB

convex quadrilateral and centroids

Source: Romanian Nationals RMO 2005 - grade 9, problem 1

March 31, 2005

ratioquadraticsgeometryanalytic geometryvectorGauss

Problem Statement

Let

ABCD

be a convex quadrilateral with

AD\not\parallel BC

. Define the points

E=AD \cap BC

and

I = AC\cap BD

. Prove that the triangles

EDC

and

IAB

have the same centroid if and only if

AB \parallel CD

and

IC^{2}= IA \cdot AC

. Virgil Nicula