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Quadrilateral with tree same sides

Source: CAPS 2024 p4

July 4, 2024
geometryIntersectionquadrilateralcyclic quadrilateral

Problem Statement

Let ABCDABCD be a quadrilateral, such that AB=BC=CD.AB = BC = CD. There are points X,YX, Y on rays CA,BD,CA, BD, respectively, such that BX=CY.BX = CY. Let P,Q,R,SP, Q, R, S be the midpoints of segments BX,CY,BX, CY , XD,YA,XD, YA, respectively. Prove that points P,Q,R,SP, Q, R, S lie on a circle.
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