Problem

Source: 2013 Oral Moscow Geometry Olympiad grades 10-11 p4

Tags: geometry, similar triangles, perpendicular, diagonals, equal segments



Similar triangles $ABM, CBP, CDL$ and $ADK$ are built on the sides of the quadrilateral $ABCD$ with perpendicular diagonals in the outer side (the neighboring ones are oriented differently). Prove that $PK = ML$.