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Mathematics of Guangzhou Senior High School Entrance Examination in 2009
24. As shown in figure 14, the square ABCD with the side length of 1 is divided into four small rectangles by two line segments EF and GH parallel to the side, which intersect at point P. (1) If AG=AE, it is proved that AF = Ah(2) If ∠ FAH = 45, it is proved that. (3) If the circumference of RT δ GBF is 1, find the area of rectangular EPHD.

25. (The full score of this small question is 14) as shown in figure 13. The image of the quadratic function intersects with the X axis at points A and B, and intersects with the Y axis at point C (0,-1). The area of Δ Δ ABC is. (1) Find the relation of quadratic function; (2) Take a point M(0, m) on the Y axis as the vertical line of the Y axis in the morning. If the vertical line of ABC has a common point with the circumscribed circle, find the range of m; (3) Is there a point D on the image of quadratic function, which makes the quadrilateral ABCD a right trapezoid? If it exists, find the coordinates of point D; If it does not exist, please explain why.