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cyclic wanted, isosceles trapezoid, // to angle bisectors related

Source: Switzerland - 2020 Swiss MO p7

December 8, 2020
geometrytrapezoidangle bisectorcyclic quadrilateral

Problem Statement

Let ABCDABCD be an isosceles trapezoid with bases AD>BCAD> BC. Let XX be the intersection of the bisectors of ∠BAC\angle BAC and BCBC. Let EE be the intersection ofDB DB with the parallel to the bisector of ∠CBD\angle CBD through XX and let FF be the intersection of DCDC with the parallel to the bisector of ∠DCB\angle DCB through XX. Show that quadrilateral AEFDAEFD is cyclic.
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