解这个题---Question Number: 10 Question Stem: 如图, 在 Rt△ACB 中, ∠ACB = 90°, AC² - BC² = 4, 点 E 是边 AB 上的中点, 连接 CE, 过点 A 作 AD ⊥ CE 交 CE 的延长线于点 D, 设 AE 长为 x, DE 长为 y, 则下列代数式的值不变的是 ( ). (As shown in the figure, in Right △ACB, ∠ACB = 90°, AC² - BC² = 4. Point E is the midpoint of side AB. Connect CE. Draw AD perpendicular to CE, intersecting the extension of CE at point D. Let AE be x, and DE be y. Then which of the following algebraic expressions has a constant value?) Options: A. x² + y² B. x² - y² C. xy D. x y Chart/Diagram Description: * Type: Geometric figure. * Main Elements: * A right-angled triangle △ACB is shown with the right angle at vertex C. * Vertices are labeled A, B, and C. * A point E is located on the hypotenuse AB. * A line segment CE is drawn. * A line segment AD is drawn such that AD is perpendicular to the extension of CE at point D. * Point D is located on the extension of CE beyond E. * Right angle symbol is shown at C (∠ACB) and at D (∠ADE or ∠ADC, since D is on the line CE extended and AD ⊥ CD). * Labels: E is on AB. D is on the line CE extended. AD ⊥ CD. * Relative Position: C is at the bottom left corner of the triangle. B is above C. A is to the right of C. E is on the line segment AB, appearing to be the midpoint (as stated in the text). The line segment CE extends towards the right. The line AD is drawn from A, intersecting the extended line CE at D, forming a right angle at D. * Lengths are implied for AE (as x) and DE (as y), but not explicitly labeled on the diagram.