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If the distance from a point on a straight line to the center of a circle is equal to the radius of the circle, then the straight line is the tangent line of the circle. B. the distance from the center of the circle to the straight line The correct one of the following propositions is () A. If the distance from a point on a line to the center of a circle is equal to the radius of the circle, the line is tangent to the circle B. If the distance from the center of the circle to the straight line is not equal to the radius, the line intersects the circle C. If a line and a circle have a unique common point, the line is tangent to the circle D. If the line AB has no intersection with the circle, then the line AB is separated from the circle PS: I feel both C and D are right~
C
D is a line segment, which can be in a circle
The distance from the center of the circle to the straight line is equal to the radius, which is a necessary condition for the line to be tangent to the circle
It is a necessary and sufficient condition
If the distance between the centers of two circles is equal to 4, the radii of the two circles are R and R respectively, and R and R are two of the equations x2-5x + 4 = 0, then the position relationship between the two circles is () A. Contains B. Exotomy C. Intersection D. Exotropism
∵x2-5x+4=0，
∴x1=4，x2=1，
∴R=4，r=1，d=4，
∴R+r=5，R-r=3，
∴3＜4＜5，
That is, R-R < d < R + R,
The two circles intersect
Therefore, C
Given that the distance between the centers of two circles d = 1.5, and the radii of two circles are the two roots of equation x minus 4x + 4 equal to 0, then the position relationship between the two circles is
x^2-4x+4=0
x1=x2=2
x1+x2=4
x1-x2=0
d=1.5
x1-x2
It is known that the distance between the centers of two circles is equal to 5, and the diameter of the two circles is the two roots of the equation x square-10x + 3 = 0. Try to judge the position relationship between the two circles
I'll give you a way
According to x square - 10x + 3 = 0, x 1 + x 2 = R1 + R2 = 10 is obtained by using the Vader theorem
10 is greater than 5
Therefore, the center distance is less than the sum of radius
Two circles intersect
If the distance d between the centers of two circles satisfies the equation | D-4 = 3, and the radius of two circles is the two roots of equation x2-7x + 12 = 0, the position relationship between the two circles is judged
Because | D-4 | = 3, D1 = 7, D2 = 1. And because x2-7x + 12 = 0, X1 = 3, X2 = 4
When d = 7, the two circles are tangent, and when d = 1, the two circles contain
If the distance between the centers of two circles is 3 and the radii of the two circles are the two roots of the equation x2-4x + 3 = 0, then the position relationship between the two circles is () A. Intersection B. Exotropism C. Contains D. Exotomy
By solving the equation x2-4x + 3 = 0, X1 = 3, X2 = 1
According to the meaning of the title, r = 3, r = 1, d = 3,
∴R+r=4，R-r=2，
2 < 3 < 4, R-R < d < R + R
The two circles intersect
Therefore, a
The radius of the two circles is two of the equation x? - 7x + 6 = 0, and the distance between the centers of the two circles is the root of the equation x? - x-20 = 0
The radii of two circles are two of the equation x? - 7x + 6 = 0
x²-7x+6=0
(x-6)(x-1)=0
x1=6;x2=1
So, the radius of the circle is 6 and 1
The center distance is the root of the equation x? - x-20 = 0
(x-5)(x+4)=0
X=5
Because 6-1 = 5
So two circles are inscribed
The radius of circle O is r, the distance from point O to line L is D, and RD satisfies the absolute value of equation [2r-7] + [D-4] ^ 2 = 0 In order to judge the position relationship between the circle and the straight line L, they are separated, intersected and tangent No and RD satisfies the equation R, D
| 2r-7 | ≥ 0 and (D-4) ° ≥ 0. | from | 2r-7 | + (D-4) ° = 0, it must be: 2r-7 = 0, D-4 = 0. Thus, r = 7 / 2, d = 4, ∵ D ﹤ R. the circle is separated from the straight line
The sum of several nonnegative numbers is equal to 0, unless every number is equal to 0
If the radius of circle O is 5cm, the distance from O to straight line L is op = 3cm, q is the point above L, PQ = 4.1cm, what is the relationship between point Q and circle O
Q is outside the circle o
RELATED INFORMATIONS
- 1. If the radius of ⊙ o is 5cm, and the shortest chord length passing through a point P in ⊙ o is 8cm, then Op=______ .
- 2. What is the chord length of the straight line y = radical 3x cut by the circle x? + y? - 4Y = 0?
- 3. If the radius of ⊙ o is 5cm and the length of chord AB is 6cm, then the distance from the midpoint of chord AB to the midpoint of inferior arc AB is______ .
- 4. It is known that the radii of the intersecting circles are 5cm and 4cm respectively, and the common chord length is 6cm
- 5. If point P is a point outside the line L, ABC is three points above L, PA = 3cm, Pb = 4cm, PC = 5cm, then the distance from point P to line L is? A.3cm B.4cm C. Less than 3cm D. no more than 3cm
- 6. Point P is a point outside the line L, a, B, C are three points on the line L, PA = 4cm, Pb = 5cm, PC = 2cm, then the distance between point P and line L () A. Less than 2cm B. Equal to 2cm C. No more than 2cm D. It's 4 cm
- 7. As shown in Fig. 1, in the plane rectangular coordinate system, point a starts from (1,0) and moves along the x-axis at the speed of 1 unit length per second In the process of motion, the rhombus oabc is made with OA as one side, so that B and C are in the first quadrant and ∠ AOC = 60 ° to connect AC and ob. At the same time, point m starts from the origin O and moves along the diagonal line ob at the speed of three unit length of the root sign per second. If the circle is drawn with point m as the center and Ma as the radius, the movement time is set as T seconds 1. When t = 1, judge the position relationship between point O and circle m, and explain the reason 2. When the circle m is tangent to the OC edge, calculate the value of T 3. With the change of T, the number of common points on the four sides of circle m and diamond oabc is also changing. Please write down the corresponding relationship between the number of common points and the size of T
- 8. In the plane rectangular coordinate system, if the center of circle P (2, a) (a > 2), radius is 2, and the length of chord ab of circle P is two 3, then the value of a is I know the answer is 2 + radical 2, but why
- 9. As shown in the figure, in the plane rectangular coordinate system, the straight line y = 4 / 3x + 8 intersects the coordinate axis at two points a and B, AE bisection angle Bao intersects the Y axis at e, and point C is a point in the first quadrant of the line y = X Find the e-coordinate of the point, AE analytic formula problem supplement: chart
- 10. In the plane rectangular coordinate system xoy, it is known that the circle m with m as the center passes through three points F1 (0, - C) F2 (0, c) a ((√ 3) C, 0), where C > 0 (1) finds the mark of circle M In the plane rectangular coordinate system xoy, it is known that the circle m with m as the center passes through three points F1 (0, - C) F2 (0, c) a ((√ 3) C, 0), where C > 0 (1) Find the standard equation of circle m (expressed by formula containing C) (2) It is known that the left and right vertices of the ellipse y ^ 2 / A ^ 2 + x ^ 2 / b ^ 2 = 1 (a > b > 0) (where a ^ 2-B ^ 2 = C ^ 2) are D, B, and the two intersections of circle m and X axis are a and C respectively, and point a is on the right side of point B, and point C is on the right side of point D. ① calculate the range of eccentricity of ellipse; ② if a, B, m, O, C, D, (o is the origin of coordinates) are uniformly distributed on the X axis in turn, Is the intersection of MF1 and df2 on a fixed line? If so, ask for the equation of the fixed line; if not, please explain the reason
- 11. How many points on the circle x ＾ 2 + y ＾ 2 + 2x + 4y-3 = 0 to the straight line x ＾ y + 1 = 0 is the root sign 2! Although there are online solutions, but I still don't understand! Please explain!
- 12. It is known that a vertex of an ellipse is a (0, - 1) and the focus is on the x-axis. If the distance between the right focus and the root of the line X-Y + 2 is 2 = 0, the distance is 3 Let the ellipse intersect with the straight line y = KX + m and have different two points m n when am = an to find the value range of M
- 13. (2006 Yantai) known: on the one variable quadratic equation X2 - (R + R) x + 1 4D2 = 0 has no real root, where R and R are the radii of ⊙ O1, ⊙ O2 respectively, and D is the center distance between the two circles, then the position relationship of ⊙ O1, ⊙ O2 is () A. Exotropism B. Tangency C. Intersection D. Contains
- 14. It is known that the straight line L is tangent to the circle C: x square + y square + 2x-4y + 4 = 0, and the distance from the origin o to L is 1, and the equation of the straight line L is obtained
- 15. It is known, as shown in the figure: in the plane rectangular coordinate system, O is the coordinate origin, the quadrilateral oabc is a rectangle, the coordinates of points a and C are a (10, 0), C (0, 4), respectively; point D is the midpoint of OA, and point P moves on the edge of BC; when △ ODP is an isosceles triangle with waist length of 5, the coordinates of point P are______ .
- 16. In the plane rectangular coordinate system, the points a (- 4,0) and B (2,0) are known. If the point C is in the first order function y = - 1 On the image of 2x + 2, and △ ABC is a right triangle, then the point C satisfying the condition has () A. 1 B. 2 C. Three D. Four
- 17. In the plane rectangular coordinate system, O is the coordinate origin. The point P (m, n) is on the image of the inverse scale function y = K / X (1) If M = k, n = K-2, find the value of K (2) If M + n = radical 2 K, Op = 2, and the inverse proportional function y = K / X satisfies: when x > 0, y decreases with the increase of X, and the value of K is calculated
- 18. As shown in the figure, in the plane rectangular coordinate system, the image of quadratic function intersects C at Y axis, a and B at x axis, points a and B are on both sides of the origin The coordinate of a is (- 3,0), Ao = co = 3BO (1) Find this quadratic function expression (2) If the point d (- 2, y) is a point on the parabola, find the area of △ BCD (3) In (2), if point P is a moving point between B and D on the parabola, when P moves to what position, the area of △ BDP is the largest? Find the coordinates of point P and the maximum area of △ BDP!
- 19. As shown in the figure, in the plane rectangular coordinate system, point O is the origin, the diagonal ob of diamond oabc is on the X axis, and the vertex A is in the inverse scale function y = 2 On the image of X, the area of the diamond is______ .
- 20. It is known that O is the origin of the plane rectangular coordinate system. The straight line passing through the point m (- 2,0) and the circle x ^ 2 + y ^ 2 = 1 intersect P and Q If the vector OP * vector OQ = - 1 / 2, find the equation of the line L If the area of the triangle OMP and the triangle OPQ are equal, find the slope of the line L