Arc AB = arc a'b'what does it mean? Are the two arcs equal or are they of equal length?

There must be some difference. A holds, B is equal in length, but the angle degree (radius) of the center of the circle corresponding to them is not necessarily the same, so the arcs are not necessarily the same, which means that they can completely coincide

In the same circle, if the arcs are equal, are the angles of the center of the circle they are facing equal? Are the chords opposite equal? Can you make sense?

For the same circle, R is equal
l = nπr/180
l =αr
If the variables of L and R in these two formulas are fixed, then of course n and α are equal
If there is a triangle formed by two chords and radius, it can be proved that the two triangles are congruent and the chords are equal naturally

Is the arc to which an equal center angle is equal

It doesn't have to be in the same circle or the same circle

If there are two points a and B on a circle, then there are () arcs in this graph. The sum of the central angles of each arc is () degree 1. If there are two points a and B on a circle, then there are () arcs in the graph. The sum of the center angles of each arc is () degree 2. The size of the arc length is determined by () and () 3. The center angle () 4. If the center angle of a circle is 30 degrees, then the arc length of the center angle is () 5. The distance between the two feet of a compass is 10 cm, so the length of the semicircle arc it draws is () cm 6. Given that the radius of the circle where an arc is located is 2 and the center angle of the circle is 45 degrees, then the length of the arc is () 7. If the arc length is 31.4 and the radius of the circle is 30, then the angle of the center of the arc is () degrees 8. If the length of an arc is 4 π and the center angle of a circle is 60 °, then the radius of the circle is () 9. Given that the length of an arc is 18.84 cm, and the angle of the center of the circle is 60 degrees, then the radius of the circle where the arc is located is () A、18 B、36 C、27 D、9 10. When the center angle of the circle is enlarged by 2 times and the radius is enlarged by 2 times, the arc length () A. 2 times B, 2 times C, 4 times D and 4 times 11. When the arc length is 1 / 4 of the original length and the center angle of the circle is unchanged, the diameter is the original () A. 1 / 2 B, 1 / 6 C, 1 / 4 / D, 1 / 8 Time is not waiting!

1. If there are two points a and B on a circle, then there are (2) arcs in this graph. The sum of the center angles of each arc is (360) degree. 2. The length of the arc is determined by (center angle) and (radius). 3. On the same circle, the center angle of two equal arcs (equal) 4. The center angle of the circle is 30 degrees

Why is the angle of the center of the circle opposite the same arc equal?

The same arc is the same arc. There is only one angle between the two ends of the arc and the center line of the circle. Therefore, it is not appropriate to say that the center angles of the same arc are equal. Equality should be for two or more quantities
There are innumerable circular angles to the same arc, all of which are equal to half of the degree of the central angle of the arc

The following proposition is correct () A. An equal center angle is equal to a chord B. The arcs to which an equal chord is equal C. Equal arcs are equal to each other D. Bisect a line perpendicular to the chord

A. In the same circle or equal circle, the chord corresponding to the equal center angle of the circle is equal, so this option is wrong;
B. In the same circle or equal circle, the arc corresponding to the equal chord is equal, so this option is wrong;
C. An equal arc is equal to a chord, correct;
D. The diameter perpendicular to the chord bisects the chord, so this option is incorrect
Therefore, C

The following proposition is true A. Equal strings are equal to arcs B. If the angle of the center of a circle is equal, the chord to which it is opposite is equal C. In the same circle or equal circle, the angle of the center of the circle is not equal, and the chords are not equal D. If a chord is equal, its angle at the center of the circle is equal

A. If the conclusion B and D are tenable, they must take "in the same circle or equal circle" as the precondition, so a, B and D are wrong;
Therefore, C

1. The following propositions are correct: (a) the chords corresponding to the equal central angles of a circle are equal B. the arcs to which the equal chords are equal C. the chords to which the equal arcs are opposite are equal D. perpendicular Explain why D. Bisect a line perpendicular to the chord

AB is not true, only in the same size circle, can hold. If the circle size is different, it does not hold. D is not complete, can not see what it means
D is not right. It should be a straight line passing through the center of the circle and perpendicular to the chord
B is right. Equal arcs mean that arcs can coincide. Arcs that can coincide must come from circles of equal size

It is known that in circle O, the circular angle of arc AB is 60 ° and that of arc CD is 60 ° and the value of AB: CD is calculated I'm sorry, I don't have a picture

Suppose the radius of the circle is r
Because the circular angle of arc AB is 60 degrees
So the center angle of arc AB is 120 degrees
So the arc length of arc AB is L = 120 / 360 * 2 π r = 1 / 3 * 2 π R
The arc length of arc CD is L = 60 / 360 * 2 π r = 1 / 6 * 2 π R
So AB: CD = 2:1

In circle O, diameter AB = 4, chord AC = 2 √ 3, chord ad = 2. Find the degree of arc CD

The arc degree is the angle degree of the center of the circle the arc is facing
Connect BC and BD, because AB is the diameter, so ∠ ACB = ∠ ADB = 90 °, so there is
Cos ∠ cab = AC / AB = √ 3 / 2, cos ∠ DAB = ad / AB = 1 / 2, so ∠ cab = 30 ° and ∠ DAB = 60 °;
When AC and AD are on the same side of AB, ∠ CAD = ∠ DAB - ∠ cab = 30 ° and arc CD = 60 °
When AC and AD are on both sides of AB, ∠ CAD = ∠ DAB + ∠ cab = 90 ° and arc CD = 180 °

Arc AB = arc a'b'what does it mean? Are the two arcs equal or are they of equal length?