帮忙讲解下这道题目---7. (2016 秋•安图县期末) 如图,在△ABC 中,AB = AC,AB 的垂直平分线交 AB 于 M,交 AC 于 N.
(1) 若∠ABC = 75°,则∠MNA 的度数是
(2) 连接 NB,若 AB = 10cm,△NBC 的周长是 18cm .
①求 BC 的长;
②在直线 MN 上是否存在 P,使由 P、B、C 构成的△PBC 的周长值最小?若存在,标出点 P 的位置并求△PBC 的周长最小值;若不存在,说明理由
Chart/Diagram Description:
* **Type:** Geometric figure (Triangle with a line).
* **Main Elements:**
* **Shape:** A triangle labeled ABC.
* **Points:** A, B, C are vertices of the triangle. M is a point on the line segment AB. N is a point on the line segment AC.
* **Lines:**
* Line segments AB, BC, AC form the triangle.
* A straight line passes through M and N. This line is depicted intersecting AB at M and AC at N. Based on the problem description, this line is the perpendicular bisector of AB and intersects AB at M and AC at N.
* A dashed line segment NB connects points N and B.
* **Labels:** Points A, B, C, M, N are labeled.