CE is independant to choice of CAB why?

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Picture from geogebra If points A , B , C are fixed and D is intersection point of two lines ( Angle bisector of A and Perpendicular bisector of BC ) let E is point on line AC such that line ED is perpendicular to line AC Then length of segment CE is determined by lengths of two segment AC and AB eg) If AB=12 AC=5 , then CE=7/2