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Angle bisectors in a trapezoid and cyclic quads

Source: St Petersburg 2022 9.3

September 28, 2022
geometry

Problem Statement

Given is a trapezoid ABCDABCD, AD∥BCAD \parallel BC. The angle bisectors of the two pairs of opposite angles meet at X,YX, Y. Prove that AXYDAXYD and BXYCBXYC are cyclic.
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