In ⊙ 0, if the length of string AB is equal to the radius, find the degree of the circumferential angle of the arc opposite string ab

Case 1: as shown in the left figure, connect OA and ob, take a point at ⊙ and connect Ca and CB,
∵AB=OA=OB，
∴∠AOB=60°，
∴∠ACB=1
2∠AOB=30°，
That is, the circumferential angle of the chord AB is equal to 30 °;
Case 2: as shown in the figure, connect OA and ob, and take a point d at any bad arc,
If ad, OD and BD are connected, ∠ bad = 1
2∠BOD，∠ABD=1
2∠AOD，
∴∠BAD+∠ABD=1
2（∠BOD+∠AOD）=1
2∠AOB，
⊙ the length of AB is equal to the radius of ⊙ o,
‡△ AOB is an equilateral triangle, ∠ AOB = 60 °,
∴∠BAD+∠ABD=30°，∠ADB=180°-（∠BAD+∠ABD）=150°，
That is, the circumferential angle of chord AB is 150 °

The chord ab of circle O divides circle O into two arcs of 1:5, then the circumferential angle of AB is?

The corresponding center angles are 360 * 1 / (1 + 5) = 60360 * 5 / (1 + 5) = 300;
The corresponding circumferential angle is half of the circle center: 30150;
360*1/(1+5)*(1/2)=30
360*5/(1+5)*(1/2)=150

In a circle with radius 3, if the chord AB is equal to 3, the arc length of AB is ()

Connecting OA and ob
Then OA = ob = 3
Because AB = 3
Triangle OAB is an equilateral triangle
So ∠ AOB = 60 °
Arc length of the whole circle = π * 2 * 3 = 6 π
Arc length of AB = 6 π * 60 / 360 = π

In a circle with radius 1, the length is equal to What is the central angle of the string of 2______ Degrees

As shown in the figure, in ⊙ o, ab=
2，OA=OB=1，
∴AB2=OA2+OB2，
‡△ AOB is a right triangle, and ∠ AOB = 90 °,
That is, the length is equal to
The central angle of the chord of 2 is 90 °
So the answer is: 90

What is the central angle of a string with a length equal to twice the root of the radius

Because a string with a length equal to twice the root of the radius
Set radius = 1
Chord length = root 2
be
Two radius chords can form an isosceles right triangle
therefore
Center angle = 90 °

In ⊙ 0, if the length of string AB is equal to the radius, find the degree of the circumferential angle of the arc opposite string ab