数学平移相关尺规作图---**Extracted Content:** **(18)** 如图, 在每个小正方形的边长为1的网格中, 点 *P*, *A* 均在格点上. (I) 线段 *PA* 的长为______; (II) 直线 *PA* 与 $\triangle ABC$ 的外接圆相切于点 *A*, $AB = BC$. 点 *M* 在射线 *BC* 上, 点 *N* 在线段 *BA* 的延长线上, 满足 $CM = 2AN$, 且 $MN$ 与射线 $BA$ 垂直. 请用无刻度的直尺, 在如图所示的网格中, 画出点 *M*, *N*, 并简要说明点 *M*, *N* 的位置是如何找到的 (不要求证明)______. **Diagram Description:** * **Type:** Geometric figure drawn on a grid. * **Background:** A grid of small squares, each with side length 1 according to the problem statement. * **Points:** Points labeled *P*, *A*, *B*, *C* are located at grid intersections. * Approximate grid coordinates (assuming bottom-left visible intersection is (0,0)): * A is at (4, 4). * P is at (5, 6). * B is at (1, 2). * C is at (6, 1). * **Lines/Segments/Rays:** * Line passing through P and A. This line appears to be tangent to the circle at A. * Segment BC. * Line passing through A and C. * Ray starting from B, passing through A, and extending beyond A (extension of segment BA). The line MN is perpendicular to this ray. * Ray BC, starting from B and passing through C. Point M lies on this ray. * Extension of segment BA, starting from A and extending away from B along the line containing segment BA. Point N lies on this extension. * **Circle:** A circle passing through points A, B, and C (the circumscribed circle of triangle ABC). * **Labels:** Points are labeled P, A, B, C. * **Caption:** "第 (18) 题" is below the diagram.