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Regional Olympiad - FBH 2012 Grade 10 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2012

September 25, 2018
geometrycircumcircle

Problem Statement

Quadrilateral ABCDABCD is cyclic. Line through point DD parallel with line BCBC intersects CACA in point PP, line ABAB in point QQ and circumcircle of ABCDABCD in point RR. Line through point DD parallel with line ABAB intersects ACAC in point SS, line BCBC in point TT and circumcircle of ABCDABCD in point UU. If PQ=QRPQ=QR, prove that ST=TUST=TU
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