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2020 IGO Intermediate P1

Source: 7th Iranian Geometry Olympiad (Intermediate) P1

November 4, 2020
trapezoidmidpointgeometryTriangleIGO

Problem Statement

A trapezoid ABCDABCD is given where ABAB and CDCD are parallel. Let MM be the midpoint of the segment ABAB. Point NN is located on the segment CDCD such that ∠ADN=12∠MNC\angle ADN = \frac{1}{2} \angle MNC and ∠BCN=12∠MND\angle BCN = \frac{1}{2} \angle MND. Prove that NN is the midpoint of the segment CDCD.
Proposed by Alireza Dadgarnia
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