How many radians is the center angle of a string with a length equal to 3 times the root of the radius Trouble = give me the process

How many radians is the center angle of a string with a length equal to 3 times the root of the radius Trouble = give me the process

Distance h from chord midpoint to circle center, radius r, chord length R √ 3,
H ²= R ²- [R√3)/2] ²= R ²- 3R ²/ 4=R ²/ 4,
H=R/2,
So the angle between the chord and the radius = 30 degrees,
The included angle between the connecting line between the chord midpoint and the circle center and the radius = 90 ° - 30 ° = 60 °,
Center angle = 60 degrees × 2 = 120 degrees × π / 180 = 2 π / 3 (radian)

If the length of the arc is equal to the side length of the regular triangle inside the circle, the number of radians of the center angle of the circle is () A. π three B. 2π three C. three D. 2

As shown in the figure, the equilateral triangle ABC is the inscribed triangle of circle O with radius R,
Then the center angle of the circle opposite to line ab ∠ AOB = 2 π
3，
As om ⊥ AB, the vertical foot is m, in RT △ AOM, Ao = R, ∠ AOM = π
3，
∴AM=
three
2r，AB=
3r，
∴l=
3 R, from the arc length formula   l=| α| r，
Well, α= l
r=
3r
r=
3．
So choose   C．

It is known that the arc length of an arc is equal to the side length of the inscribed regular triangle of its circle, then the radian number of the center angle of the arc is __

As shown in the figure,
△ ABC is an inscribed regular triangle of ⊙ o with radius r,
Then BC = 2CD = 2rsin π
3=
3r，
Let the number of radians of the center angle of the arc be α，
Then R α=
3r，
Solution α＝
3．
So the answer is:
3．

Given that the length of an arc in a circle is exactly equal to the side length of the circumscribed regular triangle of the circle, the radian number of the center angle of the arc is () A. three two B. three three C. three D. 2 three

As shown in the figure,
Let the inscribed circle of △ ABC be tangent to edge BC at point D, its center is point O, and the radius r = 1
If ob is connected, ob is equally divided into ∠ ABC and ∠ OBD = 30 °
In △ BOD, BC
2=BD=OD
tan30°=1
three
3，
The solution is BC = 2
3．
∵ the length of an arc in a circle is exactly equal to the side length of the circumscribed regular triangle of the circle,
The number of radians of the center angle of this arc is 2
3．
Therefore: D

Given that the length of an arc in a circle is exactly equal to the side length of the circumscribed regular triangle of the circle, the radian number of the center angle of the arc is () A. three two B. three three C. three D. 2 three

As shown in the figure,
Let the inscribed circle of △ ABC be tangent to edge BC at point D, its center is point O, and the radius r = 1
If ob is connected, ob is equally divided into ∠ ABC and ∠ OBD = 30 °
In △ BOD, BC
2=BD=OD
tan30°=1
three
3，
The solution is BC = 2
3．
∵ the length of an arc in a circle is exactly equal to the side length of the circumscribed regular triangle of the circle,
The number of radians of the center angle of this arc is 2
3．
Therefore: D

If the length of an arc is equal to the radius, the number of radians of the center angle of the circle opposite the arc is A.1 B.π/2 C.π/3 D.2/1

one
The angle is equal to the arc length divided by the radius