It is known that: as shown in the figure, AB is the diameter of ⊙ o, AC is the chord, CD ⊥ AB at D. if AE = AC, be intersects ⊙ o at point F, CF and de are connected

It is proved that: (1) connecting BC, ∵ AB is the diameter of ⊙ o, ∵ ACB = 90 °∵ CD ⊥ AB, ∵ ACD ∵ ABC. ∵ Acad = ABAC. ∵ AC = AE, ∵ AE2 = ad ∵ ab. (2) ∵ AE2 = ad ∵ AB, ∵ ead = ∵ Bae, ∵ ade ∵ AEB. ∵ AED = ∵ B. ∵ ACF = ? B, ? ACF = ? AED

RELATED INFORMATIONS

1. As shown in the figure, AB and AC are the chords of ⊙ o, ad ⊥ BC at D, intersection of ⊙ o at F, AE and diameter of ⊙ O. what is the relationship between the two chords be and the size of CF? Explain the reason
2. If ad ^ 2 = AE * AC, CD = CB
3. As shown in the figure, AB is the diameter of the circle O, ad = De, AE and BD intersect with point C, then there are several angles equal to angle BCE in the figure
4. As shown in the figure, AB is a semicircle, O is the midpoint of AB, C and D are on AB, and ad ‖ OC connects BC and BD. if CD = 62 °, what is the degree of ad? （　　） A. 56B. 58C. 60D. 62
5. In graph o, the strings AB and CD intersect at E. if arc ad = arc AC, we prove that AC squared = AE multiplied by ab
6. As shown in the figure, BC is the diameter of circle O, the chord AE is perpendicular to BC, the perpendicular foot is point D, arc AB = 1 / 2, arc BF, AE and BF intersect at point G, and prove that Ba is BG and B As shown in the figure, BC is the diameter of circle O, the chord AE is perpendicular to BC, the perpendicular foot is point D, arc AB = 1 / 2, arc BF, AE and BF intersect at point G, and it is proved that Ba is the middle term of the proportion of BG and BF (not shown in the figure for the time being),
7. On the plane rectangular coordinate system: about the abscissa and ordinate of two symmetrical points of the origin
8. In the plane rectangular coordinate system, given that point a (2a-b, - 8) and point B (- 2, a + 3b) are symmetrical about the origin, then the value of a · B is______ ．
9. As shown in the figure, in the plane rectangular coordinate system, a is a certain point on the negative half axis of the X axis, and a moving point B starts from the origin and moves along the Y axis at a speed of one unit per second Axis positive half axis forward ABC is isosceles Two seconds later, C (2, - 2) calculates the coordinates of point a
10. In Cartesian coordinate system, the line L1 passes through (2, 3) and (- 1, - 3), the line L2 passes through the origin o, and intersects with the line L1 at the point P (- 2, a). (1) find the value of a; (2) (- 2, a) what kind of solution of binary linear equations can be seen? (3) Let the line L1 and the y-axis intersect at point A. can you find the area of △ apo?
11. As shown in the figure, AB and AC are the chords of ⊙ o, ad ⊥ BC at D, intersection of ⊙ o at F, AE and diameter of ⊙ O. what is the relationship between the two chords be and the size of CF? Explain the reason
12. As shown in the figure, in O, the chord AB = AC = 10, the chord ad intersects BC with E, AE = 4, and the length of ad is calculated
13. As shown in the figure, in the rectangular coordinate system, point a is a point on the image of inverse scale function Y1 = KX, the positive half axis of ab ⊥ X axis is at point B, and C is the midpoint of OB; the image of primary function y2 = ax + B passes through two points a and C, and the Y axis is at point d (0, - 2), if s △ AOD = 4 (1) (2) observe the image, please point out the value range of X on the right side of y-axis when Y1 > Y2
14. When a circle passes through a (2,1) point and is tangent to a straight line X-Y = 0, and the center of the circle is on 2x-y = 0, the standard equation of the circle is obtained
15. Find out the equation of the circle which passes through a (2, - 1) and is tangent to the line x + y = 1, and the center of the circle is on the line y = - 2x. (I) find out the standard equation of the circle; (II) find out the chord length AB of the intersection of the circle in (I) and the line 3x + 4Y = 0
16. Given that the circle passes through the point P (2, - 1) and is tangent to the straight line X-Y = 1, and its center is on the straight line y = - 2x, the equation of the circle is obtained
17. Given a circle passing through point P (2, - 1), the center of the circle is on L1: y + 2x = 0 and tangent to the line L2: x-y-1 = 0, the equation of the circle is obtained
18. A circle passes through point P (2, - 1) and is tangent to the straight line X-Y = 1. The center of the circle is on the straight line y = - 2x
19. If the circle C passes through (2, - 1) and is tangent to the line x-y-1 = 0, and the center of the circle is on the line y = - 2x, then the standard equation of the circle C is
20. It is known that the center coordinate of the circle is (- 1,2) and tangent to the line 2x + Y-5 = 0 at point M. the standard equation of the circle is obtained