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If the radius of the circle is 2cm, the length of one chord in the circle is 2 3 cm, then the distance between the midpoint of the chord and the midpoint of the inferior arc is______ cm．
According to the vertical diameter theorem, it is found that half of the string is
3cm，
According to the Pythagorean theorem, the chord center distance is 1cm,
Then the distance between the midpoint of the chord and the midpoint of the inferior arc is 2-1 = 1cm
In a circle of radius 1, the length is The length of the arc to which the chord of 2 is equal to______ .
As shown in the figure, in ⊙ o, ab=
2，OA=OB=1，
∴AB2=OA2+OB2，
Ψ Δ AOB is a right triangle, and ∠ AOB = 90 °,
That is, the length is equal to
The chord of 2 has two segments: one is 90 ° to the center of the circle, and the other is 270 ° to the center of the circle,
Then the arc lengths at both ends are 90 π × 1
180=π
2，270π×1
180=3
2π．
So the answer is: π
2 or 3
2π．
The radius of the circle is known to be The center of the circle is on the line y = 2x, and the chord length of the circle cut by the line X-Y = 0 is 4 2. Find the equation of circle
Let the center of the circle (a, 2a) be set, and the chord center distance D can be obtained from the chord length formula=
10−8=
2，
From the distance formula of point to line, d = | a − 2A|
2=
Two
2|a|，
The center coordinate of the circle is (2,4), or (- 2, - 4), and the radius is
10，
The equation of the circle is: (X-2) 2 + (y-4) 2 = 10 or (x + 2) 2 + (y + 4) 2 = 10
Is 3 root 10 equal to 6 root 1
3 root 10 equals root 90
6 root sign 1 equals root 36
So three root 10 is not equal to six root sign one
Given the radius of circle O is 1cm, string AB = radical 3, AC = radical 2, find the degree of angle BAC! This problem is considered to be double solution, if yes, find two kinds of graphs,
It's a double solution. That's right
Given Ao = 1, according to the value of cosine, we know that
Above ∠ OAC = 45, ∠ OAB = 30, so ∠ BAC = 15
The following VOAC = 45, ∠ OAB = 30, so ∠ BAC = 75
Given the radius of circle O is 1cm, chord AB = root 2cm, calculate the degree of angle AOB
The triangle AOB is an isosceles triangle (OA = ob = 1)
Because OA ^ 2 + ob ^ 2 = AB ^ 2 (1 + 1 = 2)
So the angle AOB is 90 degrees
Given that ⊙ O1, ⊙ O2 intersect at points a and B, and the radii of the two circles are equal to the common chord length AB, ab = 1, find ⊙ ao1b and O1O2
∵ the radius of both circles is equal to the common chord length ab
∴AB=AO1=BO1=AO2=BO2
ν Δ abo1 and Δ abo2 are equilateral triangles
∴∠AO1B=60°
Height of regular triangle = √ 3 / 2
O1O2=2*√3/2=√3
If still have doubt, welcome to ask. Wish: study progress!
Circle O1 intersects with circle O2 at two points a and B. the radius of circle O1 is 8 cm, and that of circle O2 is 15 cm. If O1O2 = 17 cm, AB is?
Connect O1A, O2A, AB, AB to O1O2 at point C,
Because the radius of circle O1 O1A = 8 cm, the radius of circle O2 O2A = 15 cm, O1O2 = 17 cm,
So O1A ^ 2 + O2A ^ 2 = O1O2 ^ 2
So the triangle o1o2a is a right triangle, and the angle o1ao2 is 90 degrees,
Because circle O1 and circle O2 intersect at points a, B,
So O1O2 is the vertical bisector of ab,
So AB = 2Ac, and ac * O1O2 = O1A * O2A
That is: 17ac = 8 * 15
AC=120/17
So AB = 2Ac = 240 / 17 cm
Circle O1 intersects with circle O2 at two points a and B. the radius of circle O1 is 8 cm, and that of circle O2 is 6 cm. If O1O2 = 10 cm, how much 6 is ab equal to
If we connect abo1o2o1o2 and cross AB to e, then O1O2 vertically bisects AB (i.e. AE = be) and connects o1ao2art △ ao1eo1a? - o1e? = AE? Similarly, RT △ o2aeo2a? - o2e? = AE? Because o2e = (10-o1e) O1A = 8o2a = 6, all 8? - o1e? = 6
Let the radius of circle O1 and circle O2 be 3 and 2 respectively, O1O2 = 4, a and B be the intersection points of the two circles, try to find the length of common chord ab of the two circles
If O1 and O2 are connected at the intersection point of two circles, your problem can be simplified as follows: the three sides of the triangle are 2,3,4, find the height from the fixed point to the side 4. First, set the fixed point as a, make the height, the intersection point with the bottom edge is C, set CO2 as X, CO1 as y. according to the Pythagorean theorem of two triangles, we can get the equation: x + y = 4; 2 ^ 2-x ^ 2 = 3
RELATED INFORMATIONS
- 1. As shown in the figure, circle O1 and circle O2 are inscribed at point a, O2 is then circled O1, and chord AB intersects circle O1 at C. If AB = 10cm, find the length of BC
- 2. For example: the radii of circle O1 and circle O2 are 4 and 1 respectively, O1O2 = 6, P is the moving point on circle O2, and the tangent line of circle O1 is made through point P, then the shortest tangent length is? Picture It should be able to draw it
- 3. As shown in the triangle ABC, ab = 4, the circle O1 with BC as the diameter intersects AC, and D is the midpoint of AC, and de ⊥ ab. if BC ⊥ AB, circle O2 is circumscribed with circle O1, If BC ⊥ AB, circle O2 is circumscribed with circle O1, and tangent to de and be, the radius of circle O2 is calculated
- 4. Known: as shown in the figure, ⊙ O1 and ⊙ O2 intersect at a and B, point O2 is on ⊙ O1, ad is the diameter of ⊙ O2, connect dB and extend ⊙ O1 to point C Verification: 1 2AD＝ CD2−CO22．
- 5. As shown in the figure AB is the diameter of circle O, AC, AD are chords, and ab bisection angle CAD
- 6. In circle O, given the diameter AB = 2, chord AC length 1 and chord ad length root 2, then the degree of angle DAC is?
- 7. As shown in the figure, given Ao ⊥ OC, ob ⊥ OD, ∠ AOB = 142 °, calculate the degree of ∠ cod
- 8. As shown in the figure, AB is the chord of OD, and the radius OC and OD intersect AB at points E and f respectively, and AE = BF. Verify that OE = of
- 9. It is known that in circle O, the length of chord AB is three times the root of radius OA, and point C is the midpoint of arc ab. what figure is the quadrilateral oacb and why?
- 10. The radius of circle OA = 10cm, chord AB = 12cm, P is the moving point on AB, find the shortest distance from point P to center O of circle o
- 11. Given that the radius of circle O is 6 and the length of chord AB is 6 times the root sign 3, then the degree of the center angle of chord AB is?
- 12. As shown in the figure, AB and CD are the two chords of circle o
- 13. The edge ab of the square ABCD with side length of 4 is the diameter of circle O, CF is the tangent line of circle O, e is the tangent point, f is the chord of circle O on AD 1 find the area of CDF 2 find the length of line segment be
- 14. If point P is the point on the chord AB, connect OP, pass P as PC ⊥ OP, and PC intersect ⊙ o at point C. If AP = 4, Pb = 2, then the length of PC is () A. Two B. 2 C. 2 Two D. 3
- 15. As shown in the figure, in ⊙ o with diameter AB = 12, chord CD ⊥ AB is at m, and M is the midpoint of radius ob, then the length of chord CD is () A. 3 B. 3 Three C. 6 D. 6 Three
- 16. As shown in FIG. 11, AB is the diameter of circle O, passing through point o as parallel line of chord BC, tangent AP crossing point a, connecting point P and connecting AC. (1) verification: △ ABC ~ △ Poa (2) OB = 2, Op = 7 / 2, find the length of BC
- 17. At ⊙ o, C is the center of ACB, CD is the diameter, chord AB intersects CD at point P, PE is perpendicular to point E, if BC = 10, CE ratio EB = 3:2, AB is found
- 18. As shown in the figure, in the triangle ABC, ab = AC, BF = CD, BD = CE, given the angle a = 40, calculate the degree of the angle EDF
- 19. In the triangle ABC, ad is the center line on BC side, e is a point on AC, be and ad intersect F, if AE = EF, it is proved that BF = AC Here I know to extend ad, but I don't know if you can make CG through point C, hand over ad to g, make CG = DC, I don't know if this is OK. Ask!
- 20. What is the relationship between the degree of angle AEC and the degree of arc AC and arc BD? If e is outside the circle, what is the relationship between the degree of angle AEC and the degree of arc AC and arc BD?