请详细讲解这道几何题的答案---**Question Number:** 9.
**Question Stem:**
如图 10-11, 在△ABC 中, △ABC 的角平分线 OB 与角平分线 OC 相交于点 O, 过点 O 作 MN // BC, 分别交 AB, AC 于点 M, N.
**Sub-question (1):**
(1) 请写出图 10-11 中所有的等腰三角形, 并说明理由;
**Sub-question (2):**
(2) 若 AB + AC = 14, 求△AMN 的周长.
**Chart/Diagram Description:**
* **Type:** Geometric figure (Triangle).
* **Main Elements:**
* A triangle labeled △ABC.
* Point O is located inside the triangle.
* Line segment BO is drawn from vertex B to point O.
* Line segment CO is drawn from vertex C to point O.
* Line segment MN passes through point O, with point M on side AB and point N on side AC.
* Line segment MN is parallel to side BC (indicated by MN // BC in the question text).
* Vertices A, B, C are labeled.
* Points M, N, O are labeled.
* The diagram is labeled "图 10-11".
* Lines BO and CO appear to be angle bisectors based on the text description.