As shown in the figure, in the two concentric circles with o as the center, the chord AB and CD of the big circle are equal, and AB and the small circle are tangent at point E
Prove: as shown in the right figure, connect OE, make of ⊥ CD through o at f. ∵ AB and small ⊙ o tangent at point E, ∵ OE ⊥ AB, ∵ AB = CD, ∵ OE = of (the chord center distance of the same circle is equal), and ∵ CD is tangent to small ⊙ o
RELATED INFORMATIONS
- 1. As shown in the figure, in the two concentric circles with o as the center, the chord AB and CD of the big circle are equal, and AB and the small circle are tangent at point E
- 2. OA is the radius of circle O, OP is perpendicular to OA, the chord AB intersects op with C, and Pb = PC
- 3. In the circle O, the radius is 4 and the angle AOB is 60 degrees. Point C is the midpoint of arc AB, CM is vertical OA, CN is vertical ob, and the perpendicular feet are points m and N, respectively (1) (2) when point C moves on arc AB, try to judge whether the length of Mn changes and prove your conclusion (1) (2) when point C moves on arc AB, try to judge whether the length of Mn changes and prove your conclusion
- 4. As shown in the figure, ∠ AOB = 30 °, OC bisects ∠ AOB, CD ⊥ OA in D, CE ∥ Ao intersects ob in E & nbsp; & nbsp; OE = 20cm, calculate the length of CD
- 5. As shown in the figure, in RT △ AOB, the circle AB with radius OA intersects at point C. If Ao = 5, OB = 12, the length of BC is obtained
- 6. It is known that the center of circle m is on the straight line 2x-y + 5 = 0 and intersects with y axis at two points a (0, - 2), B (0,4) (1) to solve the equation of circle M (2) Find the tangent equation of circle m passing through point C (- 4,4); (3) given D (1,3), point P moves on circle m, find the trajectory equation of vertex Q of parallelogram adqp with AD and AP as a group of adjacent sides
- 7. It is known that the circle C and the y-axis intersect at two points m (0, - 2), n (0, 2), and the center of the circle C is on the straight line 2x-y-6 = 0. (1) find the equation of the circle C; (2) make a straight line through the center of the circle C, so that the line AB sandwiched between two straight lines l1:2x-y-2 = 0 and L2: x + y + 3 = 0 is exactly bisected by the point C, and find the equation of the straight line
- 8. The Y-axis of the circle center on 2x-y-7 = intersects at (0, - 4), (0, - 2), and the circle equation is solved
- 9. It is known that the center of circle C is on the straight line 2x-y-3 = 0 and passes through points a (5,2), B (3,2) Find 1. The chord length of line L passing through point P (2,1) and intersecting circle C is 2 root sign 6. Find the equation of line L 2. Let Q be the moving point on the circle C and o be the origin of the coordinate, and try to find the maximum area of OPQ of the triangle
- 10. Given that point P is a moving point on circle C: x ^ 2 + y ^ 2 + 2x = 0, a (1,0), and that the vertical line of line PA intersects the straight line PC at point m, then the trajectory equation of point m is
- 11. The radius of two concentric circles, the radius of the big circle, the opposite extension lines of OA and ob intersect the small circle at C and D respectively. It is proved that AB is parallel to CD
- 12. In RT △ ABC, ∠ C = 90 °, ab = 5, BC = 4, find the radius of inscribed circle______ .
- 13. As shown in the figure, a, B, C and D are the four points on the circle O, and the verification of AC / / BD, OA ⊥ ob is ad ⊥ BC
- 14. As shown in the figure, in the circle O with radius r, the angle AOB is equal to 2a, and OC is perpendicular to ab at point C. find the length of the chord AB and the distance between the chord centers
- 15. In the circle O, the length of the string AB is 6, and its corresponding chord center distance is 4, then the radius OA=______ .
- 16. 5. Translate the line y = 3x-2 up three units along the Y axis, then the expression of the line is
- 17. It is known that the line y = 3x-1, the analytical formula of the line after its downward translation of 3 units along the y-axis is
- 18. Move the line y = - 3x + 1 downward by 4 units and then to the right by 3 units
- 19. 1. Translate the origin three length units to the left and two length units to the down to get o ', then the coordinate of o' is 2. If the abscissa of the three vertices of △ ABC in the rectangular coordinate system remains unchanged and the ordinate decreases by two length units, it means that △ ABC is translated () units to () 3. Triangle a'b'c 'is obtained by the translation of triangle ABC. If the corresponding point of point a (- 1, - 4) is a' (1, - 1), then the corresponding coordinates of point B '(1,1) and point C are ()
- 20. The line y = 2x is shifted to the left by 3 length units to get the line (related to the function)