MathDB
point P in ABCD such that (PAB)=(PBC)=(PCD)=(PDA)

Source: 1982 Swedish Mathematical Competition p3

March 28, 2021
equal areasareasgeometry

Problem Statement

Show that there is a point PP inside the quadrilateral ABCDABCD such that the triangles PABPAB, PBCPBC, PCDPCD, PDAPDA have equal area. Show that PP must lie on one of the diagonals.