例题在四边形ABCD中,已知|ADD B|=2(3)~(1/2),|BDDC|=5,|CDD D|=3(5)~(1/2),|D DD A|=4(2)~(1/2),求ADDC·BDDD的值.分析仔细研究题设条件不难发现,四边形ABCD的四条边满足关系|ADDB|2+|CDDD|2=|BDDC|2+|DDDA|2.联想到菱形的特征,我们猜测四边形ABCD的对角线AC与对角线BD垂直.于是,我们可以利用三角方法、解析手段和向量工具,紧扣题设的数 Example In the quadrilateral ABCD, it is known that | ADD B | = 2 (3) ~ (1/2), | BDDC | = 5, | CDD D | = 3 (5) | = 4 (2) ~ (1/2), find the value of ADDC · BDDD.After careful examination of the design conditions, it is not difficult to find that the four sides of the quadrilateral ABCD satisfy the relation | ADDB | 2+ | CDDD | 2 = | BDDC | 2 | DDDA | 2. Considering the diamond features, we suspect that the diagonal AC of the quadrilateral ABCD is perpendicular to the diagonal BD. Thus, we can use triangulation, analytical tools and vectoring tools,