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Concurrency

Source: Iranian TST 2020, second exam day 2, problem 4

March 12, 2020
geometryincentercircumcircleHarmonicshomothety

Problem Statement

Let ABCABC be an isosceles triangle (AB=ACAB=AC) with incenter II. Circle ω\omega passes through CC and II and is tangent to AIAI. ω\omega intersects ACAC and circumcircle of ABCABC at QQ and DD, respectively. Let MM be the midpoint of ABAB and NN be the midpoint of CQCQ. Prove that ADAD, MNMN and BCBC are concurrent.
Proposed by Alireza Dadgarnia
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