请解释上面数学题的解题过程---25. 如图 1, 在梯形 ABCD 中, AD∥BC, AB=CD, ∠ABC=60°, AD=5, BC=13, 点 O 是对角线 BD 的中点. 点 E 为边 BC 上一动点, 连接 EO. (1) 请直接写出 AB 的长; (2) 如果点 E 为边 BC 的中点, 连接 CO, 求 △OEC 的面积; (3) 如图 2, 延长 EO 交射线 DA 于点 F, 连接 DE、BF, 如果 EF 平分 ∠BED, 求四边形 BEDF 的周长. **Diagram Descriptions:** **图 1 (Figure 1):** * Type: Geometric figure (Trapezoid). * Shape: Trapezoid ABCD. * Vertices: Labeled A, B, C, D. A is top left, D is top right, B is bottom left, C is bottom right. * Lines: AB, BC, CD, DA are sides of the trapezoid. BD is a diagonal. EO is a line segment connecting point E on BC to point O on BD. * Points: A, B, C, D are vertices. O is on BD. E is on BC. * Relationships: AD appears parallel to BC. AB appears equal to CD. O is shown on BD. E is shown on BC, located between B and C. * Annotation: "图 1" is labeled below the figure. **图 2 (Figure 2):** * Type: Geometric figure (Trapezoid with extended lines). * Shape: Trapezoid ABCD with AD parallel to BC. Ray DA is extended. * Vertices: Labeled A, B, C, D, E, F. A and D are on the upper line/ray. B, E, C are on the lower line segment. F is on the extension of DA, to the left of A. * Lines: AB, BC, CD are sides of the trapezoid. DA is the upper base line. EF is a line segment passing through O and connecting E on BC and F on ray DA. BD is a diagonal. DE and BF are line segments. * Points: A, B, C, D are vertices. O is the intersection of BD and EF. E is on BC. F is on ray DA. * Relationships: AD is part of the line containing F and A and D, which appears parallel to BC. E is on BC. O is on BD and EF. F is on the ray DA, beyond A. * Annotation: "图 2" is labeled below the figure.