Given that the length of an arc on circle O is equal to the side length of the inscribed square of the circle, find the radians of the center angle of the circle to which this arc is opposite

The diagonal length of the inscribed square is 2R
Then the side length of the square is: 2R * (root sign 2 / 2) = (root sign 2) r
The arc length is also (root 2) r
Arc length = center angle * radius
Therefore, the corresponding center angle should be (root sign 2) radians

1. If the length of an arc is equal to the side length of its inscribed regular triangle, the number of radians of its center angle is 2. In acute triangle ABC, SINB = 1 / 3, then cos (a + C)=

1. Set the radius as R and the side length of the inscribed regular triangle as √ 3R. According to the arc length = radius * arc center angle. √ 3R = R* α So the radian of the center angle is α= √ 3 2. The sum of triangle internal angles is π cos (a + C) = cos (π - b) = - cos (b), and according to sin2b + cos2b = 1 and ∠ B is acute angle, CoSb = √ (1-1 / 9) = 2 √ 2 / 3, so cos (a

If the length of an arc is equal to the side length of the inscribed regular triangle of its circle, the radian number of its center angle a (0, π) is?

Radians = a * circle radius
Side length of inscribed regular triangle = root 3 * circle radius
(the center angle of the circle where the inscribed regular triangle is located is 120 °)
So the number of radians is: root 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

In the sector, the arc length of the center angle is equal to half of the radius, then the radian number of the center angle is?

[(r/2)/2 Л r]*2 Л= 1/2

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 on circle O is equal to the side length of the inscribed square of the circle, find the radians of the center angle of the circle to which this arc is opposite