MathDB

Let

ABCD

be a quadrilateral, such that

AB = BC = CD.

There are points

X, Y

on rays

CA, BD,

respectively, such that

BX = CY.

Let

P, Q, R, S

be the midpoints of segments

BX, CY ,

XD, YA,

respectively. Prove that points

P, Q, R, S

lie on a circle.

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