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If the distance between the centers of the two circles is d = 8, and the lengths of the radii of the two circles are the two roots of the equation x ^ - 7x + 12 = 0, then what is the positional relationship between the two circles? Please explain the reason! In a hurry
It is found that the radius of two circles is five and seven. Eight is greater than seven minus five and less than seven plus five, so they intersect
If the radii R and R of the two circles are exactly the two roots of the equation x? - 4x + 2 = 0, and the distance between the centers of the two circles is d = 3, then the position relationship between the two circles is
Because (2 + radical 2) + (2-radical 2) = 4 > 3, the two members intersect
The radii of ⊙ O1 and ⊙ O2 are two of the equations x2-7x + 11 = 0, respectively. If the two circles are circumscribed, then the value of center distance a is______ .
From the equation x2-7x + 11 = 0, X1 + x2 = 7,
According to the meaning of the title, two circles are circumscribed, a = X1 + x2 = 7
It is known that the absolute value of the intercept of the straight line L on the x-axis and y-axis is equal, and the distance to the point (1,2) is the root sign 2
Answer: y = x + 3 or y = X-1 or y = - x = 5 or y = - x = 1
R. R is the radius of two circles (r > R) and D is the distance between the centers of two circles Then the position relation of two circles with radius R and R is
x² - 2Rx + r² = d(2r-d)x² - 2Rx + r² - 2dr + d² = 0x² - 2Rx + R² + r² - 2dr + d² - R² = 0(x - R)² + (r² - 2dr + d² - R²) = 0 x = R...
We know the equation about X: RX + M = (2r-1) x + 4 when what value of RM is: 1. The equation has unique solution; 2. The equation has countless solutions; 3. The equation has no solution
The original formula can be reduced to (R-1) x = M-4
① If there is a unique solution, then R-1 is not equal to 0, then R is not equal to 1
② If there are infinite solutions, then R-1 = 0 and M-4 = 0, then r = 1, M = 4
③ If there is no solution, then R-1 = 0 and M-4 does not = 0, then r = 1, M is not equal to 4
Solve the equation | X-1 | + | x + 2 | = 5. From the geometric meaning of absolute value, the equation represents the value of X corresponding to the point where the sum of the distances between 1 and - 2 is 5. On the number axis, the distance between 1 and - 2 is 3, and the corresponding point of X is on the right of 1 or the left of - 2. If the corresponding point of X is on the right side of 1, we can see that x = 2; similarly, if the corresponding point of X is on the left side of - 2, we can get x = - 3, so the original square is x = - 3 The solution of the equation is x = 2 or x = - 3 Refer to the readings and answer the following questions: (1) The solution of equation | x + 3 | = 4 is______ . (2) Solve the inequality | x-3 | + | x + 4 | ≥ 9; (3) If | x-3 | + | x + 4 | ≥ a holds for any x, find the value range of A
(1) The solution of the equation | x + 3 | = 4 is from the point on the number axis to - 3. The distance is the number represented by the points of 4 unit length, which are 1 and - 7
So the solutions are 1 and - 7;
(2) From the geometric meaning of the absolute value, the equation represents the value of X corresponding to the point where the sum of the distances from 3 and - 4 on the number axis is greater than or equal to 9
On the number axis, X ≥ 4 or X ≤ - 5 can be obtained
(3) | x-3 | + | x + 4 | is the sum of the distances from the point of X to the number axis and 3 and - 4,
When the point representing the corresponding x is between 3 and - 4 on the number axis, the sum of the distances is the smallest, which is 7
Therefore, a ≤ 7
If the maximum distance between o point and the point on the circumference is 5cm and the minimum distance is 1cm, then the radius of the circle is______ .
The point O should be divided into two cases: inside and outside the circle
When the point O is in the circle, the diameter is 5 + 1 = 6cm, so the radius is 3cm;
When the point O is outside the circle, the diameter is 5-1 = 4cm, so the radius is 2cm
So the answer is: 3 or 2cm
It is known that the radius of circle O is 5cm and the radius of circle P is 1cm. Circle O is tangent to circle P. when circle P rotates around circle O, the distance that point P passes through is______ I want to ask for it at 22:07 12 / 01 at 22:30 12 / 01
1: Inscribed s = 2 * r * m = Pi
=2*(5-1)*m
=25.12(cm)
2: Circumscribed s = 2 * r * m = Pi
=2*(5+1)*m
=37.68(cm)
Answer
Given that the radius of circle O is 5cm, P is a point in the circle, and op = 1cm, the shortest chord length of the chord passing through point P is
Pass through point P as chord CD perpendicular to op
Then CD is the shortest string
∵OA=5,OP=1
According to Pythagorean theorem, CP = 2 √ 6
∴CD=4√6
The shortest chord is 4 √ 6cm
RELATED INFORMATIONS
- 1. It is known that the radius of ⊙ o is 5cm, the point P is the outer point of ⊙ o, Op = 8cm. A circle with P as the center is tangent to ⊙ o, and the radius of the circle is______ cm．
- 2. Find the chord length cut by the square of circle x + the square of Y-2 times the root sign 2x-4y-2 = 0 on the x-axis
- 3. Given that the radius of a circle is 5 and the length of a chord is 8, what is the distance between the midpoint of the chord and the midpoint of the arc corresponding to the chord
- 4. Given that the radius of circle O is ob = 5cm, chord AB = 6cm, D is the midpoint of arc AB, the length of chord BD is calculated
- 5. As shown in the figure: in a circle with a diameter of 10 cm, the distance from the center of the circle to the chord AB is 4cm
- 6. If a, B and C are on a straight line, and the line segment AB = 5cm and BC = 4cm, what is the distance between a and C?
- 7. With a calculation method, the negative 3,2,1 and 0,1,2,3,4,5 are changed into 8,3,0 negative 1 and 0,3,8,15,24 It turns negative 3 2 1 and 0 1 2 3 4 5 into 8 30 and negative 0 3 5 15 24
- 8. As shown in the figure, in the plane rectangular coordinate system, points a (6,0), B (0,8). If point P moves at a speed of 1 unit / second from point Ao, point Q moves at a speed of 2 units / second along ob direction from point O, and P and Q start at the same time After how long, the area of △ OPQ is 5? Can the area of △ OPQ reach 10? Why? I'm sorry, I can't post pictures
- 9. As shown in the figure, two concentric circles with point o as the common center are known. The chord ad of the large circle intersects the small circle B and C. If ad = 6cm, BC = 4cm, calculate the area of the ring
- 10. In the plane rectangular coordinate system, the Y-axis of a (- 4,0) B (1,0) whose diameter is ab and C (0,2) is the tangent intersection of a circle. The legitimate axis of X and D are used to find the coordinates of D
- 11. The distance from each point on the circle to the center of the circle is equal to______ The points whose distance from the center of the circle is equal to the radius are all in the______ .
- 12. Two circles with the same radius intersect, and the distance between the centers of the two circles is exactly equal to the radius of 10 cm
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- 15. It is known that the eccentricity of the ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is the root 5 / 3, and the distance from one end point of the minor axis to the right focus is 3
- 16. If there is no real root in the quadratic equation x ^ 2 + (M + 2) x + (1 / 4) m ^ 2 = 0, the root number m ^ 2 + │ M-1 │
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- 19. Find the distance between the parallel lines 3x-2y-5 = 0 and 6x-4y + 3 = 0
- 20. It is known that the radii R1 and R2 of the two circles are two of the equations x2-7x + 10 = 0, and the distance between the centers of the two circles is 7, then the position relationship between the two circles is______ .