OC in circle O is perpendicular to ab AB = 16 sinaoc = 3 / 5 calculate radius OA of circle O and chord center distance OC calculate cosaoc tanaoc
In △ AOC
sin∠AOC=AC/AO=3/5
And AC = AB / 2 = 8
Substituting
AO=40/3
The solution of Pythagorean theorem is OC = 32 / 3
cos∠COA=OC/AO=4/5
tan∠AOC=AC/OC=3/4
RELATED INFORMATIONS
- 1. The diameter of the circle O of BD, OA perpendicular to ob, M is a point on the inferior arc AB, the tangent MP of the circle O crosses through point m, the extension line of OA intersects at point P, and the intersection of MD and OA intersects at point n 1. Verify PM = PN. 2. If BD = 4, PA = two-thirds Ao, make BC ∥ MP through point B, intersect circle O at point C, and find the length of BC.
- 2. As shown in the figure, it is known that in RT △ ABC, the radius of the inscribed circle is 3cm and the radius of the circumscribed circle is 12.5cm, so the three sides of △ ABC can be calculated
- 3. As shown in the figure, circle O is the inscribed circle of triangle ABC, and the tangent points are D, e, F. the known angles BCA = 90 degrees, ad = 5cm, DB = 3cm. Find the area of triangle ABC D is on AB, e is on BC, f is on AC
- 4. If the side length of equilateral △ ABC is 3cm, the radius of its inscribed circle is
- 5. As shown in the figure, the radius of the inscribed circle of RT △ ABC is 1 cm, and the hypotenuse is tangent to the circle O at point D. given AB = 5, find the length of AD and AC
- 6. As shown in the figure, BD is the diameter of ⊙ o, OA ⊥ ob, M is the point on the inferior arc AB, through point m as the tangent of ⊙ o, the extension line of OA at point P, MD and OA at point n. (1) verification: PM = PN; (2) if BD = 4, PA = 32ao, through point B as BC ∥ MP intersection ⊙ o at point C, the length of BC
- 7. As shown in the figure, BD is the diameter of ⊙ o, OA ⊥ ob, M is the point on the inferior arc AB, through point m as the tangent of ⊙ o, the extension line of OA at point P, MD and OA at point n. (1) verification: PM = PN; (2) if BD = 4, PA = 32ao, through point B as BC ∥ MP intersection ⊙ o at point C, the length of BC
- 8. As shown in the figure, the center of two concentric circles is O, the radius of big circle O is OA, OB intersects small circle O with C, D, please explain: AB / / CD I hope we don't use center angle and circle angle
- 9. 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
- 10. As shown in the figure, it is known that in △ AOB, ∠ AOB = 90 ° OD ⊥ AB is at point D. the circle with point o as the center and OD as the radius intersects OA at point E, intercept BC = ob on Ba, and prove that CE is the tangent of ⊙ o
- 11. Given the radius of ⊙ o OA = 5, the chord center distance OC of chord AB = 3, then AB = () A. 4B. 6C. 8D. 10
- 12. In the circle O, M is the middle point of the chord AB, passing through the point B as the tangent of the circle O, and intersecting with the extension line of OM at the point C. proof 1: angle a = angle C. If OA = 5, OB = 8, find OC
- 13. In the plane rectangular coordinate system, e. f starts from point O, and moves along the positive direction of x-axis at the speed of 1 unit / s, while f moves along the positive direction of y-axis at the speed of 2 units / s, and does not (4,2) make a circle with be as the diameter (1) If e and f start at the same time, let EF and ab compare with G, which is to judge the position relationship between G and circle, and prove that (2) Under the condition of (1), when FB is connected, B is tangent to the circle for a few seconds
- 14. In the plane rectangular coordinate system, it is necessary for the line y = 2x to move 3 units to the left
- 15. Given that the line y = 3x + 1, translate the line up two units along the y-axis, and then to the right three units, and find the analytical expression of the line after two times of translation
- 16. The analytic expression of the straight line y = - 3x + 1 is obtained by moving up one unit, and then moving right three units
- 17. The analytical expression of the straight line y = 3x + 1 is obtained by translating 2 units to the right and 3 units to the down______ .
- 18. First, the point P (- 2,1) is translated one length unit to the left, and then two length units to the up to get the point P, then the coordinate of P is
- 19. In a plane rectangular coordinate system, given points a (- 4,0), B (0,2), now translate line AB to the right, so that a coincides with coordinate 0, then the coordinate of B after translation is___
- 20. In the plane rectangular coordinate system, given the points a (4,5) and B (4,1), translate the line AB to the right by 5 length units (1) Try to find the area swept by line ab (2) Change the line AB to the broken line ACB, the coordinates of points a and B remain unchanged, C is (2,2), and try to find the area swept by the broken line (3) If the coordinates of points a and B remain unchanged and the coordinates of point C are changed to (1,3), does the area swept by the broken line change? (4) If the coordinates of points a and B remain unchanged and the broken line ACB is changed into a curve, does the area swept by the curve change?