MathDB
Circumscribed quadrilateral and lengths

Source: 239 MO 2024 S5

May 22, 2024
geometry

Problem Statement

A quadrilateral ABCDABCD has an incircle Γ\Gamma. The points X,YX, Y are chosen so that AX−CX=AB−BCAX-CX=AB-BC, BX−DX=BC−CDBX-DX=BC-CD, CY−AY=AD−DCCY-AY=AD-DC and DY−BY=AB−ADDY-BY=AB-AD. Given that the center of Γ\Gamma lies on XYXY, show that AC,BD,XYAC, BD, XY are concurrent.
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