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intersecting parallelograms , intersecting diagonals problem

Source: 2018 Oral Moscow Geometry Olympiad grades 8-9 p1

July 25, 2019
geometryparallelogramdiagonal

Problem Statement

Two parallelograms are arranged so as it shown on the picture. Prove that the diagonal of the one parallelogram passes through the intersection point of the diagonals of the second. https://cdn.artofproblemsolving.com/attachments/9/a/15c2f33ee70eec1bcc44f94ec0e809c9e837ff.png