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泰州2013中考数学卷第25题:如图1,矩形ABCD中,点P在边CD上,且与C、D不重合,过点A作AP的垂线与CB的延长线相交于点Q,连接PQ,M为PQ的中点.(1)求证:△ADP∽△ABQ;(2)若AD=10,AB=20,点P在边CD上运动,设DP=x,BM2=y,求y与x的函数关系式,并求线段BM长的最小值;(3)若AD=10,AB=a,DP=8,随着a的大小的变化,点M的位置也在变化.当点M落在矩形ABCD外部时,求a的取值范围.
As shown in Figure 1, in rectangle ABCD, point P is on the side CD, and does not coincide with C and D. When point A is over, the perpendicular of AP and the extension of CB intersect at point Q, Connect PQ, M is the midpoint of PQ. (1) Verify: △ ADP ∽ △ ABQ; (2) If AD = 10, AB = 20, Find the function of y and x and find the minimum length of line segment BM. (3) If AD = 10, AB = a, DP = 8, the position of point M will also change as the size of a changes. When the point M falls outside the rectangle ABCD, find the value of a range.