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How to deal with such problems as how many times the radius of a circle, how many times its diameter, how many times its circumference and how many times its area? I will have the final exam tomorrow. Is there any formula?
For example, if the radius is expanded by 2 times, then the diameter will be expanded by 2 times, the perimeter will be expanded by 2 times, and the area will be expanded by 4 times. That is to say, the expansion times of diameter and perimeter are the same as that of radius, and the area expansion is the square of radius expansion
If the radius of a circle is increased by 5 times, the diameter will be enlarged by () times, the circumference will be expanded by () times, and the area will be expanded by () times
5,5,25
When the radius of a circle is increased to three times of its original size, its diameter will be enlarged to () times, its circumference will be expanded to () times, and its area will be expanded To the original () times
When the radius of a circle is increased to three times of its original size, its diameter will be enlarged to (3) times of its original size, its circumference will be expanded to (3) times of its original size, and its area will be expanded to (9) times of its original size
When the radius of a circle is three times larger, its diameter will be enlarged by () times, its circumference will be expanded by () times, and its area will be expanded by () times
When the radius of a circle is three times larger, its diameter is (3) times larger, its circumference is (3) times larger, and its area is (9) times larger
When the radius of a circle is increased by four times, how many times has its circumference expanded and how many times its area has expanded. When the radius of a circle has been expanded by four times, how many times has its circumference been expanded
If the radius of a circle is r, its circumference is 2 * pi * r, and its area is pi * r * R1. After 4 times of increase, it is 5R, then the circumference becomes 2 * pi * (5R), that is, the circumference is expanded by 5 times; similarly, the area is pi * (5R) * (5R), that is, the area is enlarged by 25 times
The radius of the circle is doubled and its circumference is enlarged to the original______ . it's enlarged to its original size______ .
Let the radius of the original circle be r, then the diameter is 2R, the circumference of the circle is 2 π R, the area of the circle is π R2, the radius of the circle is 2R, the diameter of the circle is 4R, the circumference of the circle is 4 π R, the area of the circle is (2R) 2 π = 4 π R2, the circumference is expanded to the original 4 π R △ 2 π r = 2, the area is expanded to
The radius of a circle is doubled and its circumference is enlarged______ The area is enlarged to the original______ Times
If the radius of the original circle is r, then the diameter is 2R,
The circumference of the circle is 2 π R,
The area of the circle is π R2,
When the radius is doubled, the radius of the circle is 2R and the diameter of the circle is 4R,
The circumference of the circle is 4 π R,
The area of the circle is: (2R) 2 π = 4 π R2,
The circumference is expanded to 4 π R △ 2 π r = 2,
The area is enlarged to 4 π R2 △ π R2 = 4;
A: the perimeter is doubled and the area is quadrupled
So the answer is: 2, 4
Given that the center of the circle is at the origin of coordinates, the radius is 3 √ 3, and the coordinates of point a are (4,3), then the position relationship between point a and circle is () A. Point a is on ⊙ O. B. point a is outside ⊙ o C. Point a is in ⊙ O. D. point a is at the origin of coordinates 3√3＝5.196152423
The distance between point C and the center of the circle is 5, which is less than the radius 3 √ 3,
If the radius length of two circles is 6 and 2, and the distance between centers is 3, then the position relationship between the two circles is () A. Exotropism B. Tangency C. Intersection D. Contains
∵ the radii of the two circles are 6 and 2 respectively, and the center distance of the two circles is 3,
And ∵ 6-2 = 4, 4 ᙽ 3,
The position relationship between the two circles is contained
Therefore, D
For ⊙ o with radius 5, the center of the circle is at the origin o, and the position relationship between point P (- 3, 4) and ⊙ o is () A. In ⊙ o B. On ⊙ o C. Outside ⊙ o D. Not sure
Connect Op
∵P（-3，4），
According to Pythagorean theorem, Op=
32+42=5，
∵ radius of circle 5,
The P is on the circle o
Therefore, B
RELATED INFORMATIONS
- 1. The coordinates of the center P of a circle (- 2,5), and its radius is 6, then the origin of the coordinates is at point P
- 2. In the plane rectangular coordinate system xoy, let the image of quadratic function f (x) = x ^ 2 + 2x + B have three intersections with the two coordinate axes, and the circle passing through these three intersections is marked as C (I) find the equation of circle C; (II) set point a is a fixed point passed by circle C (its coordinates are independent of B). Ask whether there is a constant k such that the straight line y = KX + K and circle C intersect at points m, N, and | am | = | an |. If it exists, find the value of K; if not, please explain the reason
- 3. In the plane rectangular coordinate system, the distance from the point P (- 3, - 4) to the X axis is () and the distance from the point to the Y axis is
- 4. If the chord length of the straight line 2x-y + 1 = 0 and the section circle x? 2 + y? 2 = R? 2 is equal to 5, find the radius of the circle
- 5. It is known that the distance from point a (2m + 1,3m-5) to the x-axis is twice the distance from the point to the y-axis
- 6. It is known that m (x, y) is a set of inequalities where x is greater than or equal to 0, less than or equal to root 2, y is less than or equal to 2, and X is less than or equal to root sign 2Y If point a (root 2,1), then z = vector OM, the maximum value of point multiplication vector OA is
- 7. The function is equal to the root x + 4, and the value range of the independent variable x is
- 8. Given that ⊙ O1 and ⊙ O2 are circumscribed at point a, the radius of ⊙ O1 is r = 2, and the radius of ⊙ O2 is r = 1, then the circle with radius 4 has () A. 2 B. Four C. Five D. 6
- 9. Given that the length of a chord is equal to the radius r, find: (1) The length of the inferior arc to which the string is directed; (2) The area of the bow formed by this chord and minor arc
- 10. In a rectangular coordinate system, a point whose abscissa and ordinate are integers is called a lattice point. Given that the center of a circle is at the origin and its radius is equal to 5, then the grid point on the circle has______ One
- 11. When the radius of a circle is several centimeters, its circumference and area are equal
- 12. As shown in the figure, it is known that AB is the diameter of ⊙ o, AC is the chord, and bisection ⊥ bad, ad ⊥ CD, and the perpendicular foot is d Proof: CD is tangent of ⊙ o
- 13. As shown in the figure, in △ ABC, D is a point on AC, e is a point on CB extension line, and AC BC＝EF DF， Confirmation: ad = EB
- 14. As shown in the figure, the straight line DF intersects with AB and AC on both sides of △ ABC at two points D and e respectively, and intersects with the extension line of BC at point F, ∠ B = 50 °, 1 = 76 °, f = 3
- 15. In the RT triangle ABC, the angle ABC = 90 degrees, the circle O with the diameter of AB intersects AC with D, and the tangent passing through D intersects BC with e. it is proved that de = 1 / 2 BC, If Tan angle c = root 5 divided by 2, de = 2, find ad
- 16. As shown in the figure, it is known that AB is the chord of ⊙ o, the radius OA = 20cm, ∠ AOB = 120 ° and the area of ⊙ AOB is obtained
- 17. As shown in the figure, the diameter of ⊙ o is ab = 10, C and D are two points on the circle, and AC＝ CD＝ Let the tangent ed of point d cross the extension line of AC at point F. connect OC to ad at point G (1) Confirmation: DF ⊥ AF (2) Seek the length of OG
- 18. It is known that, as shown in the following four graphs, circle O1 and circle O2 intersect at two points a and B, the line CD passing through point a intersects with circle O1 at C, intersects with circle O2 at D, and straight line ef? 2 passing through point B As shown in the following figure, circle O1 and circle O2 intersect at two points a and B, the line CD passing through point a intersects with circle O1 at C, and with circle O2 at D. the line EF passing through point B intersects with circle O1 at e and circle 02 at F, so as to verify CE ∥ DF Picture in space photo album
- 19. Given that AB and CD are two diameters of circle O, chord CE / / AB, angle COE = 50 degrees, then the acute angle DOB =?
- 20. It is known that: as shown in the figure, take the oblique edge ab of RT △ ABC as the diameter to make ⊙ o, and D is the point on ⊙ o, and there is AC = CD. Pass through point C to make the tangent of ⊙ o, and connect CD with the extension line of BD at point E (1) Try to judge whether be and CE are perpendicular to each other, please explain the reason; (2) If CD = 2 5，tan∠DCE=1 2. Find the radius length of ⊙ o