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concurrent wanted, ABCD cyclic with AB + CD = BC

Source: Switzerland - Swiss MO 2004 p9

July 19, 2020
geometrycyclic quadrilateralconcurrentconcurrency

Problem Statement

Let ABCDABCD be a cyclic quadrilateral, so that ∣AB∣+∣CD∣=∣BC∣|AB| + |CD| = |BC|. Show that the intersection of the bisector of ∠DAB\angle DAB and ∠CDA\angle CDA lies on the side BCBC.
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