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一目 已知:在△ABC中,AB=10. (1)如图1,若点D、E分别是AC、BC边的中点,求DE的长. (2)如图2,若点A1、A2把4C边三等分,过A1、A2作AB的平行线,分别交BC边于点B1、B2,求A1B2+A2B2的值. (3)如图3,若点A1、A2、…、A10把AC边十一等分,过各点作AB边的平行线,分别交BC边于点B1、B2、…、B10,根据你所发现的规律,直接写出A1B2+A2B2+…+A10B10的结果. (2004年江苏省南通市中考题)
One item is known: In ΔABC, AB=10. (1) As shown in Fig. 1, if points D and E are respectively the midpoints of AC and BC sides, find the length of DE. (2) If Fig. 2, if point A1 , A2 divides the 4C side into three equal parts, passes A1, A2 as the parallel lines of AB, respectively passes BC sides at points B1 and B2, and finds the value of A1B2+A2B2. (3) If Fig. 3, points A1, A2, ... , A10 divides the AC side eleven into equal parts, passing each point as the parallel line of the AB side and handing the BC side to the point B1, B2, ..., B10. According to the rule you found, write A1B2+A2B2+... +A10B10 directly. The results. (2004 Nantong City, Jiangsu Province)