Geometry · Convex quadrilaterals · Diagonals · Extremal configurations · Counterexamples
Convex quadrilaterals \(ABCD\) and \(PQRS\) are given, where the vertices of the quadrilateral \(PQRS\) lie on the sides or in the interior of the quadrilateral \(ABCD\).
Can the sum of the diagonals of \(PQRS\) be greater than the sum of the diagonals of \(ABCD\)?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition (Okruzno takmicenje) 2019, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source