Perpendicular diagonals in convex quadrilateral
Source: Kyrgyzstan 2012, Problem 3
May 2, 2013
complex numbersgeometry unsolvedgeometry
Problem Statement
Prove that if the diagonals of a convex quadrilateral are perpendicular, then the feet of perpendiculars dropped from the intersection point of diagonals on the sides of this quadrilateral lie on one circle. Is the converse true?