Divide a circle into equal parts and make an approximate rectangle. It is known that the circumference of this rectangle after splicing is 6 cm longer than the circumference. Find the circumference and area of this circle.
It is known that A (0, 1) B (2,1) C (3,4) D (-1,2) asks whether four points are on a circle.
It is known that triangle ABC is inscribed with circle O, point D is on the extension line of OC, sinb= 1/2, ∠ D = 30.
1. Prove that AD is the tangent of circle O.
2. If AC=6, find the length of the advertisement.
It is known that the moving circle passes through the point f (-5,0) and is tangent to the circle x * x+y * y-10x-1= 0, and the trajectory equation of the moving center is found.
◎ On the left is a ring. The radius of the inner circle is 10 cm, and the radius of the outer circle is 15 cm. What is its area?
Think about it: the area of this ring is actually the area of two circles ().
(1) External circle area:
(2) Inner ring area:
(3) Area of the ring:
Note (the square of the number after x, y)
It is known that any point on the circle C: x2+y2+2x+ay-3 = 0 (A is a real number) and the symmetrical points of the straight line L: x-y+2 = 0 are all on the circle C. How much is A?
It is known that △ABC is inscribed in ○O, point D is on the extension line of OC, and sinB=? ∠ d = 30 (1) Prove that AD is the tangent of χ O (2) If AC=6, find the length of AD.
The vertex of a given regular hexagon is a, and its side length is.
If the lateral expansion of the cylinder is a square with a side length of 4cm, then the radius of the circle at the bottom of the cylinder is =.
If the inscribed circle area of a square is πcm2, its circumscribed circle area is.
1. Given a (-2,0), B (0 0,2) and c is any point on the circle x 2+y 2-2x = 0, what is the maximum ABC area of the triangle?
2. If the straight line 2ax-by+2 = 0 (a >; 0, b>0) always bisects the circumference x 2+y+2x-4y+1= 0, then the minimum value of 1/a+ 1/b is
Cd is the diameter of circle O, with D as the center and the length of od as the radius. The intersection of circle O at two points A and B proves that arc AC = CB = a b.
A cylindrical barrel with a bottom diameter of 28 cm and a height of 60 cm. Known weight per liter of water 1 kg. How many kilograms of water can this barrel hold?
1。 If two tangents are perpendicular to each other from a point outside the circle, and the distance from that point to the center of the circle is 4, then the radius of the circle is?
2。 Circle O cuts the BC side of triangle ABC at D, and cuts the extension lines of AB and AC at E and F. The circumference of triangle ABC is 18, so AE=?
3。 The ground radius of the cylinder is 3, and the length of the bus is 3, so what is the area of the side development diagram of this cylinder?
4。 The height of the cone is three times that of the root number 3, and the side development diagram is a semicircle. Find: the ratio of the generatrix of the cone to the radius of the ground; The size of the cone angle; Surface area of cone (key process)
∠ cab = 30, BC = 2, O and H in Rt△abC are the key points of AB side and AC side respectively. Rotate △ABC Rao point B 120 degrees clockwise to the position of triangle A 1BC 1, then the area (shadow area) of the scanned part of line segment OH in the whole rotation process.
It is known that point P is on line segment AB and point O is on the extension line of line segment AB. Make a circle with point O as the center, op as the radius and point C as a point on the circle O. ..
If AP=m, m is a constant, > 1, BP= 1, and op is the proportional mean of OA-ob, when point C moves on circle O, AC: BC is expressed by the formula of m..
As shown in the figure: It is known that the side AB of the rectangular ABCD passes through the center O, and points E and F are the intersections of the side AB, CD and the circle O, AE = 3cm, AD = 4cm, DF = 5cm, so find the diameter of the circle O..
It is known that point A is the sextant ON circle O, point B is the midpoint of arc AN, and point P is the moving point on radius On. If the radius of circle O is 1, find the minimum value of AP+BP.
As shown in the figure, triangle ABC, angle acb = 90, angle b = 60, CD⊥AB, vertical foot D, BD= root number 3, center C, root number 2 and root number 3 are radius left circle C. Try to judge the positional relationship between A, D and B and circle C respectively.
1. The two sides of a right triangle are 5cm and12cm respectively. Find the perimeter of the circumscribed circle and the area of the inscribed circle.
What is the ratio of the radius of inscribed circle to the radius of circumscribed circle of isosceles right triangle?
Given ⊙9 1 and ⊙ 965 (2), what shape triangle △PBC did you find? Please write the conclusion of the discovery and prove it.
It is known that AB is the diameter of ⊙O, and AE is equally divided.
(1) Verification: CD is the tangent of ⊙ o.
(2) If CB=2 and CE=4, find the length of AE.
It is known that the radius length of circle O 1 and circle O2 are r and r(R is greater than r) respectively, and the center distance is d. If the two circles intersect, try to find the root of the equation about X: (the square of x)-2 (d-r) x+(the square of r) =0.
At RT△ABC, angle C = 90, angle B = 30, O is a point on AB, OA=m, and the radius of circle O is R. What is the relationship between R and M?
AC intersects with circle o?
AC is tangent to circle o?
AC and circle o are separate?
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