(3) This problem can be solved by using the idea of transformation, and 2/3BP can be done by using the similarity. As shown in the figure, take point G, so that AG=2/3AB, cross G as GH//BP, cross H as AO, obviously △AGH∽△ABP, so AG=2/3AB=4cm, and AH=2/3AP=2t cm. To convert it into the minimum value of the folded line segment, you need to translate △AGH to make A and C coincide, and the corresponding point of G is G'. Because AH=CQ=2t cm, H and Q coincide, which is converted into the minimum value of AQ+QG'. Obviously, AQ+QG' is the minimum value of the three-point * * line, that is, the length of the line segment AG', which is in △AOG' +OG? )=√( 16? + 10? ) =2√89 cm, so the minimum value is 2√89 cm.

Thematic map