1. In △ABC, if the median line CD=3 on the side of AB is 3, AB is 6 and BC+AC is 8, then the area of △ABC is-
2。 As shown in figure 1. It is known that △ABC is an equilateral triangle with a side length of 4, BC is on the X-axis, point D is the midpoint of BC, point A is in the first quadrant, the positive semi-axis of AB and Y-axis intersects with point E, point B (-1, 0), and point P is the moving point on AC (P does not coincide with points A and C).
(1)(2 points) Find the coordinates of point A and point E;
(2)(2 points) If y=? After passing through point A and point E, find the analytical formula of parabola.
(3)(5 points) Connect PB and PD, and let L be the circumference of △PBD. When l takes the minimum value, find the coordinates of point P and the minimum value of L, and judge whether point P is on the parabola found in (2) at this time. Please fully explain your reasons for judgment.
3。 As shown in Figure 2, point D is a point ⊙O on the extension line of diameter CA, point B is on ⊙O, and AB = AD = ao.
(1) Prove that BD is the tangent of ⊙ o. 。
(2) If point E is a point on the lower arc BC, AE and BC intersect at point F,
And the area of △BEF is 8, cos∠BFA= = three-thirds? Find the area of △ACF.
4。 As shown in Figure 3, in the plane rectangular coordinate system, quadratic function? The vertex of the image is point d,
It intersects with the Y axis at point C, and intersects with the X axis at points A and B. Point A is on the left side of the origin, and the coordinate of point B is (3,0).
OB=OC？ ，tan∠ACO=？ .
(1) Find the expression of this quadratic function.
(2) The straight line passing through points C and D intersects the X axis at point E. Is there such a point F on this parabola, and the quadrilateral with points A, C, E and F as its vertices is a parallelogram? If it exists, request the coordinates of point f; If it does not exist, please explain why.
(3) If the straight line parallel to the X axis intersects the parabola at two points, M and N, and the circle with the diameter of MN is tangent to the X axis, find the length of the radius of the circle.
(4) As shown in Figure 4, if the point G(2, y) is a point on the parabola and the point P is a moving point on the parabola below the straight line AG, when the point P moves to what position, what is the largest area of △APG? Find the coordinates of point P and the maximum area of △APG at this time.