附图中的题目为初中几何题，请分析和解答该题目---**Extracted Content:** **Question 1:** **Question Stem:** 如图, 已知四边形 ABCD 为等腰梯形, AD // BC, AB=CD, AD = √2, E 为 CD 中点, 连接 AE, 且 AE=2√3, ∠DAE=30°, 作 AE ⊥ AF 交 BC 于 F, 则 BF= ( ) **Translation of Question Stem:** As shown in the figure, given quadrilateral ABCD is an isosceles trapezoid, AD is parallel to BC, AB equals CD, AD = √2, E is the midpoint of CD, connect AE, and AE = 2√3, ∠DAE = 30°. Draw AF such that AE is perpendicular to AF, and AF intersects BC at F. What is the length of BF? **Options:** A. 1 B. 3 - √3 C. √5 - 1 D. 4 - 2√2 **Chart/Diagram Description:** * **Type:** Geometric figure representing an isosceles trapezoid with additional internal line segments. * **Main Elements:** * **Shape:** A quadrilateral ABCD is depicted, which is an isosceles trapezoid. * **Vertices:** * A: Top-left vertex. * B: Bottom-left vertex. * C: Bottom-right vertex. * D: Top-right vertex. * **Edges/Sides:** * AD: The top base, appears parallel to BC. * BC: The bottom base. * AB: The left non-parallel side. * CD: The right non-parallel side. * **Internal Points and Segments:** * E: A point on the side CD, positioned visually as the midpoint. * F: A point on the base BC, located between B and C. * Segment AE: Connects vertex A to point E on CD. * Segment AF: Connects vertex A to point F on BC. * **Implied Geometric Properties (from question stem):** * AD is parallel to BC. * AB = CD (isosceles trapezoid property). * E is the midpoint of CD. * AE is perpendicular to AF (∠EAF = 90°). * Specific angle ∠DAE = 30°. * **Lengths (from question stem):** * AD = √2 * AE = 2√3