生成这道题目解题视频---**Question:** 1. 如图：点 P 是∠AOB内一定点，点 M、N 分别在边 OA、OB上运动，若∠AOB=45°，OP=3√2，则△PMN的周长的最小值为______． **Translation:** 1. As shown in the figure: Point P is a fixed point inside ∠AOB, points M and N move on sides OA and OB respectively. If ∠AOB=45° and OP=3√2, then the minimum value of the perimeter of △PMN is ______. **Given Information:** * Point P is a fixed point inside angle AOB. * Points M and N move on rays OA and OB respectively. * ∠AOB = 45° * OP = 3√2 **Question Asked:** * Find the minimum value of the perimeter of triangle PMN (PM + MN + NP). **Diagram Description:** * Type: Geometric figure. * Elements: * Vertex O. * Ray OA extending from O. * Ray OB extending from O, forming an angle ∠AOB at O. * Point P located inside the angle ∠AOB. * Line segment OP connecting O and P. * Point M located on ray OA. * Point N located on ray OB. * Triangle PMN formed by line segments PM, MN, and NP. * Labels: O, A, B, P, M, N are labeled on the corresponding points. * Relative positions: P is inside ∠AOB. M is on OA. N is on OB. O is the vertex. OA and OB are sides of the angle.