only 1 of 4 contructed vertices of # lies on the interior of convex ABCD
Source: Sharygin 2005 finals 10.1
August 29, 2019
geometryparallelograminteriorconvex quadrilateral
Problem Statement
A convex quadrangle without parallel sides is given. For each triple of its vertices, a point is constructed that supplements this triple to a parallelogram, one of the diagonals of which coincides with the diagonal of the quadrangle. Prove that of the four points constructed, exactly one lies inside the original quadrangle.