Poland 7
Source: IMO LongList 1959-1966 Problem 37
September 2, 2004
geometryparallelogramcyclic quadrilateralIMO ShortlistIMO Longlist
Problem Statement
Show that the four perpendiculars dropped from the midpoints of the sides of a cyclic quadrilateral to the respective opposite sides are concurrent.
Note by Darij: A cyclic quadrilateral is a quadrilateral inscribed in a circle.