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rhombus.

Source: Romanian TST 1978, Day 1, P4

September 28, 2018
geometryperimeterrhombusPure geometry

Problem Statement

Diagonals AC AC and BD BD of a convex quadrilateral ABCD ABCD intersect a point O. O. Prove that if triangles OAB,OBC,OCD OAB,OBC,OCD and ODA ODA have the same perimeter, then ABCD ABCD is a rhombus. What happens if O O is some other point inside the quadrilateral?
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