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2001 KJMO P8 distance between a line and a point

Source: 2001 KJMO

June 29, 2024
geometryConcyclic

Problem Statement

ABCDABCD is a convex quadrilateral, both ∠ABC\angle ABC and ∠BCD\angle BCD acute. EE is a point inside ABCDABCD satisfying AE=DEAE=DE, and X,YX, Y are the intersection of ADAD and CE,BECE, BE respectively, but not X=AX=A or Y=DY=D. If ABEXABEX and CDEYCDEY are both inscribed quadrilaterals, prove that the distance between EE and the lines AB,BC,CDAB, BC, CD are all equal.
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