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As shown in the figure, points a, O and B are on the same straight line, ∠ AOC = 1 / 2 ∠ BOC + 30 °, OE bisects ∠ BOC, and calculates the degree of BOE I don't know how to draw or dictate a straight line. The right side is B and the left side is a. there is o point in the middle, with o as the point, extending from the upper right corner to e and from the upper left corner to C~
Because a, O and B are on the same straight line, ∠ AOC + ∠ BOC = ∠ AOB = 180 ° i.e. ∠ AOC = 180 °- ∠ BOC from ∠ AOC = 1 / 2 ∠ BOC + 30 °, we can get 180 ° - ∠ BOC = 1 / 2 ∠ BOC + 30 ° so, ∠ BOC = 100 ° OE bisection ∠ BOC, so, ∠ BOE = 1 / 2 ∠ BOC = 50 °
As shown in the figure, the angle AOB = 180 ° od and OE are bisectors of the angle AOC and the angle BOC respectively, and the angle doc is 30 ° larger than the angle Coe. calculate the degree of the angle AOE
If AOB = 180 ° and OD and OE are bisectors of AOC and BOC respectively, then ∠ AOC + ∠ BOC = 180 ∠ AOC = ∠ AOD + ∠ doc = 2 ∠ doc ∠ BOC = ∠ COE + ∠ BOE = 2 ∠ EOC, then ∠ AOC + ∠ BOC = 180 = 2 ∠ doc + 2 ∠ EOC, then ∠ doc + ∠ EOC = 90, because ∠ doc - ∠ EOC = 30, then ∠ doc = 60 ∠ EOC = 3
As shown in the figure, ∠ AOB = 120 °, OD bisection ∠ BOC, OE bisection ∠ AOC. ① calculate the degree of ∠ EOD. ② if ∠ BOC = 90 °, calculate the degree of ∠ AOE
(1) ∫ AOB = 120 °, OD bisection ∫ BOC, OE bisection ∫ AOC, ∫ EOD = ∫ doc + ∫ EOC = 12 (∫ BOC + ∫ AOC) = 12 × 120 ° = 60 °; (2) ∫ AOB = 120 °, ∫ BOC = 90 °, ∫ AOC = 120 ° - 90 ° = 30 °, ∫ OE bisection ∫ AOC, ∫ AOE = 12 ∫ AOC = 12 × 30 ° = 15 °
RELATED INFORMATIONS
- 1. As shown in the figure, it is known that OE is the bisector of ∠ AOB, and C is a point in ∠ AOE. If ∠ BOC = 2 ∠ AOC, ∠ AOB = 114 °, calculate the degree of ∠ BOC. ∠ EOC
- 2. As shown in the figure, the straight lines AB and CD intersect at the points o, OE and of, which are bisectors of ∠ AOC and ∠ AOD respectively. It is known that ∠ BOC = 70 ° to find the degree of ∠ DOF and ∠ Coe
- 3. As shown in the figure, it is known that OD bisects BOC and OE bisects AOC, if BOC = 70 ° and AOC = 50 ° (1) Calculate the degree of AOB and its complement angle (2) Request the degree of ∠ doc and ∠ AOE, judge whether ∠ DOE and ∠ AOB are complementary, and explain the reason The DOA is a right angle, 90 degrees, and the diagram is drawn by myself
- 4. Given the angle AOB = 130 degrees, OE bisecting angle BOC, of bisecting angle AOC, calculate the degree of angle EOF
- 5. As shown in the figure: the parabola intersects the x-axis at two points a (- 1,0) and B (3,0), and intersects the y-axis at points c (0, - 3). Let the vertex of the parabola be d (1) find the analytical formula of the parabola and the coordinates of vertex D: (2) prove that the center of the circumscribed circle of △ BCD falls at the midpoint of the BD side: (3) if point P is a moving point on the coordinate axis, it can make the triangle with P, a, C as the vertex similar to △ BCD? If it exists, Please write the coordinates of point P: if not, please explain the reason
- 6. Given that the line L: y = x + m and parabola y2 = 8x intersect at two points a and B, (1) if | ab | = 10, find the value of M; (2) if OA ⊥ ob, find the value of M
- 7. Let a and B be two points on the parabola X & # 178; = 2PY. The line AB passes through the focus F. if the vector OA * the vector ob = - 6, solve the parabolic equation
- 8. It is known that the symmetry axis of parabola y = AX2 + BX + C = - 1, intersects with X axis at two points a and B, intersects with y axis at C, where a (- 3,0), C (0,2) (1) Finding the function relation of parabola (2) Finding the coordinates of point B (3) There is always a point P on the symmetry axis, so that the perimeter of the triangle PBC is minimum, and the coordinates of point P are requested en
- 9. It is known that the parabola y = x & # 178; - 6x + 5 (1) is the analytic expression of the parabola with respect to the y-axis symmetric image (2) is the analytic expression of the parabola with respect to the x-axis symmetric image
- 10. Parabola y = - 2x ^ + 3x-5 about x-axis, y-axis, origin after the symmetrical movement of the functional equations are? Hope to explain the knowledge points, need specific steps
- 11. As shown in the figure, the straight line AB; CD intersects at the point O, OE, bisecting the angle AOC, and the angle BOC - ∠ BOD = 18 ° to find the degree of ∠ BOE
- 12. Given that the distance from a point P on the parabola y2 = 16x to the x-axis is 12, then the distance from P to the focus f is equal to 12______ ．
- 13. The left focus of the ellipse is (√ 3,0), and the right vertex is d (2,0). Let a (1,1 / 2) be a moving point on the ellipse. If P is a moving point on the ellipse, find the trajectory equation of the midpoint m of the line PA
- 14. If P (2,2) is the midpoint of AB, then the equation of parabola C is______ ．
- 15. It is known that the center of ellipse C is at the origin and the focus is on the x-axis. The coordinates of a vertex B of ellipse C are (0,1) and the eccentricity is equal to 22. The line L with slope 1 intersects ellipse C at two points m and n. (1) find the equation of ellipse C; (2) ask whether the right focus F of ellipse C can be the center of gravity of △ BMN? If possible, find out the equation of line L; if not, explain the reason
- 16. Let a straight line passing through the focus of the parabola y2 = 2px (P > 0) intersect with the parabola. Let the coordinates of the two intersections be a (x1, Y1) and B (X2, Y2) respectively. Prove: (1) y1y2 = - P2 (2) x1x2 = p24
- 17. How to find the directrix and focus of parabola? How to find the known parabola, collimator and focus? It is how to deduce the focal point and collimator of a parabola, or how to deduce a parabola from the focal point and collimator, just as the elliptic standard equation is derived by arithmetic and algebra.
- 18. Let a (x1, Y1), B (X2, Y2), then x1x2 =? Let a (x1, Y1) and B (X2, Y2) pass through the focus of the parabola (x ^ 2) = 4Y to make the chord AB, then what is X1 times x2? There is a process or a graph.
- 19. If the distance between a point P and its focus on the parabola x ^ 2 = 4Y is 2, then the distance between point P and its directrix is 2
- 20. If the distance from a point m on the parabola x ^ 2 = - 16y to the focus is 6, then the coordinate of M is