Problems(1)
A convex quadrilateral ABCD is given. Let Oa be the circumcenter of the triangle DBC, and define Ob,Oc and Od similarly. The points Oa,Ob,Oc,Od are the vertices of a convex quadrilateral. Prove that its area is equal to half of the absolute value of the difference between the areas of AObCOd and BOcDOa.Proposed by V. Dubrovsky Kvantgeometryareas