MathDB

2020.7

Part of Swiss NMO - geometry

Problems(1)

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

Source: Switzerland - 2020 Swiss MO p7

12/8/2020
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.
geometrytrapezoidangle bisectorcyclic quadrilateral