In right triangle ABC, angle C is the right angle, and BC = 162. Point D on side AB is connected by a line segment with point E on side AC such that line segment DE is parallel to side BC and CE = 2AE. What is the length of line segment DE?

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In right triangle ABC, angle C is the right angle, and BC = 162. Point D on side AB is connected by a line segment with point E on side AC such that line segment DE is parallel to side BC and CE = 2AE. What is the length of line segment DE?