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已知:矩形ABCD中,M为BC边上一点, AB=BM=10,MC=14,如图1,正方形EFGH的顶点E和点B重合,点F、G、H分别在边AB、AM、BC上.如图2,P为对角线AC上一动点,正方形EFGH从图1的位置出发,以每秒1个单位的速度沿BC向点C匀速移动;同时,点P从C点出发,以每秒1个单位的速度沿CA向点A匀速移动.当点F到达线段AC上时,正方形EFGH和点P同时停止运动.设运动时间为t秒,解答下列问题: (1)在整个运动过程中,当点F落在线段AM上和点G落在线段AC上时,分别求出对应t的值; (2)在整个运动过程中,设正方形 与 重叠部分面积为S,请直接写出S与t之间的函数关系式以及自变量t的取值范围; (3)在整个运动过程中,是否存在点P,使 是以DG为腰的等腰三角形?若存在,求出t的值;若不存在,说明理由.
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