Rhombus
Source: Indian RMO 2005 Problem 1
February 28, 2006
geometryrhombusparallelogramcomplex numbers
Problem Statement
Let ABCD be a convex quadrilateral; P,Q, R,S are the midpoints of AB, BC, CD, DA respectively such that triangles AQR, CSP are equilateral. Prove that ABCD is a rhombus. Find its angles.