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一、质点运动型例1将一副三角尺如图1所示拼接:含30°角的三角尺(△ABC)的长直角边与含45°角的三角尺(△ACD)的斜边恰好重合.已知AB=231/2,P是AC上的一个动点.(1)当点P运动到∠ABC的平分线上时,连接DP,求DP的长;(2)当点P在运动过程中出现PD=BC时,求此时∠PDA的度数;(3)点P运动到什么位置时,以D,P,B,Q为顶点的平行四边形的顶点Q恰好在边BC上?求出此时DPBQ的面积.
First, the particle sports example 1 will be a triangular ruler as shown in Figure 1 stitching: a triangle with a 30 ° angle (△ ABC) and the long side of the square with a 45 ° angle (△ ACD) bevel just right (1) When point P moves to the bisector of ∠ABC, connect DP and find the length of DP; (2) When point P is in the range of (3) When the point P moves to any position, the vertex Q of the parallelogram whose vertexes are D, P, B and Q happens to be on the edge BC? Obtain the area of DPBQ at this moment.