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angle chasing candidate, <ADB =< PDC wanted, circumcircle related

Source: Czech-Polish-Slovak Junior Match 2013, Team p4 CPSJ

March 21, 2020
geometrycircumcircleequal anglesAngle Chasing

Problem Statement

Let ABCDABCD be a convex quadrilateral with ∠DAB=∠ABC=∠BCD>90o\angle DAB =\angle ABC =\angle BCD > 90^o. The circle circumscribed around the triangle ABCABC intersects the sides ADAD and CDCD at points KK and LL, respectively, different from any vertex of the quadrilateral ABCDABCD . Segments ALAL and CKCK intersect at point PP. Prove that ∠ADB=∠PDC\angle ADB =\angle PDC.
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