帮我解答这道题目---**Extraction Content:**
**Question Stem:**
提示: (含相似)
(2021 深圳) 8. 在正方形 ABCD 中，等腰直角△AEF，∠AFE=90°，连接 CE，H 为 CE 中点，连接 BH、BF、HF，发现 BF/BH 和 ∠HBF 为定值。
**Part (1):**
(1) ① BF/BH = √5
② ∠HBF = 45°
③ 小明为了证明①②，连接 AC 交 BD 于 O，连接 OH，证明了 OH/AF 和 BA/BO 的关系，请你按他的思路证明①②。
**Part (2):**
(2) 小明又用三个相似三角形 (两个大三角形全等) 摆出如图 2，BD/AD = EA/FA = k, ∠BDA = ∠EAF = θ (0° < θ < 90°)。
求① FD/HD = k (用 k 的代数式表示)
② FH/HD = √(k²-4kcosθ+4) (用 k、θ 的代数式表示)
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**Chart/Diagram Description:**
**Chart 1 (图1):**
* **Type:** Geometric figure.
* **Main Elements:**
* **Shapes:** A square labeled ABCD. A triangle labeled AEF, which is an isosceles right triangle with ∠AFE=90°.
* **Points:** Vertices of the square A, B, C, D. Vertices of the triangle A, E, F. Point H is located on segment CE, explicitly stated as the midpoint of CE. Point O is the intersection of the diagonals AC and BD of the square.
* **Lines/Segments:**
* Sides of the square ABCD.
* Diagonals of the square AC and BD, intersecting at O.
* Segments forming triangle AEF: AE, EF, AF.
* Additional segments: CE, BH, BF, HF.
**Chart 2 (图2):**
* **Type:** Geometric figure.
* **Main Elements:**
* **Shapes:** A quadrilateral labeled ABCD. A triangle labeled AEF.
* **Points:** Vertices of the quadrilateral A, B, C, D. Vertices of the triangle A, E, F. Point H is shown on segment CE. There is a handwritten label 'M' near the segment AD.
* **Lines/Segments:**
* Sides of the quadrilateral ABCD.
* Segments forming triangle AEF: AE, EF, AF.
* Additional segments: CE, BH, BF, HF, DF, DH.
* A line segment is drawn from D passing through M. A line segment is drawn from C to B. A line segment is drawn from D to H. A line segment is drawn from B to F. A line segment is drawn from D to F.