IMO 2019 Shortlist G5

Let ABCDE be a convex pentagon with CD “ DE and =EDC ‰ 2 ¨ =ADB. Suppose that a point P is located in the interior of th...

IMO 2019 Shortlist G5

Category: Geometry

Problem

Let ABCDE be a convex pentagon with CD “ DE and =EDC ‰ 2 ¨ =ADB. Suppose that a point P is located in the interior of the pentagon such that AP “ AE and BP “ BC. Prove that P lies on the diagonal CE if and only if areapBCDq areapADEq “ areapABDq areapABPq. (Hungary)