The third degree of the sixth root is not equal to 5:10 of the third part of the root sign

The third degree of the sixth root is not equal to 5:10 of the third part of the root sign

∵ 5 / 3 of root sign: 10 = 1 / 2 √ 3 = √ 3 / 6
﹤ the root three of the sixth is equal to 5:10 of the third of the root

As shown in the figure, the radius of ⊙ o is 1cm, and the lengths of strings AB and CD are respectively 2 cm, 1 cm, then the acute angle α between the strings AC and BD=______ Degree

Connect OA, ob, OC, OD,
∵OA=OB=OC=OD=1，AB=
2，CD=1，
∴OA2+OB2=AB2，
△ AOB is an isosceles right triangle,
Delta cod is an equilateral triangle,
∴∠OAB=∠OBA=45°，∠ODC=∠OCD=60°，
∵∠CDB=∠CAB，∠ODB=∠OBD，
∴α=180°-∠CAB-∠OBA-∠OBD=180°-∠OBA-（∠CDB+∠ODB）=180°-45°-60°=75°．

0

So △ OAB is an isosceles right triangle
If Ao is extended to meet the circle D, then CAD is a right triangle, ad = 2. There is AC = ad * cos ∠ Cao = 2cos30 degree = √ 3cm

Given that the radius of ⊙ o is 1cm, and the chord AB = root 2cm, then the central angle AOB of the chord AB is?

AO=1 ,BO=1
AB = radical 2
AO^2+BO^2=1+1=2
AB^2=2
AO^2+BO^2=AB^2
The triangle AOB is a right triangle
Center angle AOB = 90 degrees

Circle O1 and circle O2 are two equal circles, they intersect at two points a and B, and O1A = AB = 4, then the angle ao1b is equal to, and O1O2 is equal to, What figure is quadrilateral o1ao2b

60 degrees
4 root sign 3

It is known that ⊙ O1 and ⊙ O2 intersect at a and B, and O1O2 intersects AB at point C, O1A = 10, O2A = 17, ab = 16______ .

As shown in the figure,

The radius of circle O1 and circle O2 are 3cm and 4cm respectively. If O1O2 satisfies the following conditions, what is the relationship between circle O1 and circle 2 （1） 0102=8cm （2）0102=7cm （3）=5cm （4）0102=1cm (5) 0102 = 0.5cm (6) 01 and 02 coincide

10102 > 01 + 02
20102 = 01 + 02 circumcision
30102 < 01 + 02 intersection
40102 = o2-o1 endotangent
501026, coincide, circle O1 and O2 are concentric circles

It is known that the radii of ⊙ O1 and ⊙ O2 are 5cm and 8cm respectively O1O2=12cm O1O2=2cm O1O2=3cm O1O2=1.5cm O1O2=15cm O1O2=13cm

r=5cm,R=8cm
Let the distance between the centers of two circles be d
① D = 12cm, R-R < d < R + R, is intersection
② D = 2cm, D ＜ R-R, is inclusion
③ D = 3cm, d = R-R, is inscribed
④ D = 1.5cm, d < R-R, is the connotation
⑤ D = 15cm, d > R + R, is the phase separation
⑥ D = 13cm, d = R + R, circumscribed
Please give me the best

As shown in Fig. 1, the circle O1 with unequal radii is separated from the circle O2, and the line O1O2 intersects the circle O1 respectively. Circle O2 is at point A.B. and Mn is the internal common tangent point of the two circles As shown in Fig. 1, ⊙ O1, ⊙ O2 with different radii are separated, and line O1O2 intersects ⊙ O1 ⊙ O2 at points a and B, Mn is the internal common tangent point of two circles, respectively cut ⊙ O1, ⊙ O2 at points m, N. connect Ma, Nb Try to judge the quantitative relationship between ∠ amn and ∠ BNM, and prove your conclusion

Let the intersection of Mn and ab be P
Connected with o1m, o2n
o1mn=90
o2nm=90
BNM and amn are tangent angles
2amn=mo1a,2bnm=no2b
Mpo1 = npo2, o1mn = o2nm
So mo1a = no2b
amn=bnm

Given that the radius of circle O1 and circle O2 are 3 and 5 respectively, and there is no intersection point between circle O1 and circle O2, then the range of O1O2 is

The inscribed 5-3 = 2 is equal to the center distance of the circle