similar quads wanted, 4 circumcenters related
Source: Polish MO Recond Round 1987 p6
September 9, 2024
geometrysimilaritysimilar
Problem Statement
We assign to any quadrilateral the centers of the circles circumscribed in the triangles , , , . Prove that if the vertices of a convex quadrilateral do not lie on the circle, thena) the four points assigned to quadrilateral Q in the above manner are the vertices of the convex quadrilateral. Let us denote this quadrilateral by ,b) the vertices of the quadrilateral do not lie on the circle,c) quadrilaterals and are similar.