As shown in the figure, known quadrilateral ABCD is diamond, de ⊥ AB, DF ⊥ BC, please explain the quantitative relationship between be and BF

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• 1. As shown in the figure, in the plane rectangular coordinate system, the area of rectangular ABCO is 15, the side OA is larger than OC by 2. E is the midpoint of BC, the ⊙ o 'intersection X axis with OE as the diameter is at point D, and DF ⊥ AE is at point F through point D. (1) calculate the length of OA and OC; (2) prove that DF is the tangent of ⊙ o'
• 2. As shown in the figure, in the plane rectangular coordinate system, the line y = 23x - 23 intersects with the edges OC and BC of the rectangular ABCO at points E and f respectively. If OA = 3 and OC = 4 are known, then the area of △ CEF is () A、6 B、3 C、12 D、 43
• 3. In the plane rectangular coordinate system, the area of △ CEF when the line y = 2 / 3x-2 / 3 intersects with the edge OC and BC of rectangular ABCO and points E and F are known as OA = 3 and OC = 4 respectively
• 4. As shown in the figure, oabc is a rectangular piece of paper, where OA = 8 and OC = 4. Through folding, point C coincides with point a, and the crease is ef (1). Find out the length of OE (2) And prove (3) whether there is a moving point P in the straight line where EF is located, so that the value of | pb-pc | is the maximum. If not, please explain the reason; if so, calculate the coordinates of point P
• 5. In the rectangular coordinate system, there is a rectangle oabc, OA = 2, OC = 1, and the coordinate of point P is (0, - 1) (1) Finding the function analytic expression of the straight line PB (2) If the line L passing through P intersects with BC, and the ratio of the area of the rectangular oabc divided into parts is 1:4, the analytic function of the line L is obtained
• 6. There are seven planes with the same distance from the four vertices of the space quadrilateral ABCD
• 7. ABCD is a square with side length of 4, e and F are the midpoint of AB and ad, GC is vertical to plane ABCD, GC is equal to 2, find the distance from B to plane EFG?
• 8. Let e be the midpoint of AD, a right: b right = 2:3, and find the value of Ag: GC
• 9. Let e be the midpoint of AD, a right: b right = 2:3, and find the value of Ag: GC
• 10. In the parallelogram ABCD, e is the midpoint of CD, connect be and extend it, intersect the extension line of ad with point F, and prove that e is the midpoint of BF and D is the midpoint of AF
• 11. As shown in the figure, it is known that the quadrilateral ABCD is a diamond, f is the intersection of a point DF on AB, AC is on e, and it is proved that ∠ AFD = ∠ CBF
• 12. It is known that, as shown in the figure, the quadrilateral ABCD is a diamond, f is a point on AB, DF intersects AC with E
• 13. As shown in the figure, two pieces of paper of equal width are crossed and overlapped. The overlapped part is a quadrilateral. Is ABCD a diamond? Is it a proof, not a reason
• 14. As shown in the figure, is the quadrilateral ABCD obtained by superposition of two rectangles of equal width a diamond? Prove your conclusion An engineering team is planning to repair BM every day. Due to weather, cm (C
• 15. As shown in the figure, two pieces of paper of equal width are crossed and overlapped, and the quadrilateral ABCD of the overlapped part is______ Shape
• 16. As shown in the picture, two pieces of paper of equal width are crossed and overlapped. Is the overlapped part ABCD a diamond? Please prove it
• 17. The side length of the square ABCD is a. place a vertex of the square omnp large enough on the symmetric center O of the square ABCD The side length of square ABCD is a Operation and calculation: place a vertex of the square omnp large enough on the symmetric center O of the square ABCD, and OM ⊥ BC, Op ⊥ DC. Try to find the area of the quadrilateral OECF of the overlapping part of two squares Thinking and exploration: if the square omnp is rotated at any angle around point O, is be equal to CF? Why? Can we find the area of quadrilateral OECF? What do you find?
• 18. The vertex B and C of square ABCD are on the positive half axis of X axis, and a and D are on the parabola y = - 2 / 3x & # 178; + 8 / 3x
• 19. In the plane rectangular coordinate system, the coordinates of vertex B and D in square ABCD are (0,0), (2,0) respectively, and a and C are symmetric about X axis Finding the coordinates of two points a and C (using different methods)
• 20. Known: as shown in the figure, in the plane rectangular coordinate system xoy, the side length of square ABCD is 4, its vertex a moves on the positive half axis of X axis, and vertex D moves on the Y axis (points a and d do not coincide with the origin), B and C are in the first quadrant, diagonal AC and BD intersect at point P, connecting Op Q: when OA