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Geometry - Iran

Source: Iran National Olympiad 2017, Second Round, Problem 2

April 20, 2017
geometrytrapezoid

Problem Statement

Let ABCDABCD be an isosceles trapezoid such that AB∥CDAB \parallel CD. Suppose that there exists a point PP in ABCDABCD such that ∠APB>∠ADC\angle APB > \angle ADC and ∠DPC>∠ABC\angle DPC > \angle ABC. Prove that AB+CD>DA+BC.AB+CD>DA+BC.
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