1问题引入题目:如图1,点P是∠AOB内一定点,点M,N分别在边OA,OB上运动,若∠AOB=45°,OP=32~(1/2),则△PMN的周长的最小值为__。解:如图2,作P关于OA,OB的对称点C,D,联结OC,OD,则当M,N是CD与OA,OB的交点时,△PMN的周长最短,最短值是CD的长。因为P,C关于OA对称,所 1 problem introduction problem: As shown in Figure 1, point P is a certain point in ∠ AOB, point M, N respectively in the side OA, OB movement, if ∠ AOB = 45 °, OP = 32 ~ The minimum PMN circumference is __. Solution: As shown in Figure 2, for the symmetry points C and D of OA and OB and the links OC and OD, when M and N are the intersection of CD and OA and OB, the circumference of △ PMN is the shortest and the shortest is CD Long. Because P, C about OA symmetry, the