In the circle center o with radius of 50 mm, chord AB is 50 mm long. Calculate the degree of angle AOB and calculate the distance from point O to ab by using the vertical diameter theorem

In the circle center o with radius of 50 mm, chord AB is 50 mm long. Calculate the degree of angle AOB and calculate the distance from point O to ab by using the vertical diameter theorem

The triangle OAB is an equilateral triangle with angle AOB = 60 ° and a vertical line segment is drawn from point O to ab. according to Pythagorean theorem, the root sign 3 of 25 times is obtained

Calculation: 1) the distance between point O and AB, 2) the degree of AOB

Vertical diameter theorem?
Connect OA, make AB vertical line through point O and intersect AB with M
According to the vertical diameter theorem, am can be calculated as 25mm
According to Pythagorean theorem (OA = om + AM)
That is: 2500 = om square + 625
Om can be obtained
（2） OM＝OA＝OB
So) ∠ AOB = 60 degrees
PS: bisect the chord perpendicular to the diameter of the chord and bisect the arc to which the chord is bisected

As shown in the figure, in ⊙ o with radius of 50, the length of chord AB is 50, (1) Find the degree of ∠ AOB; (2) Find the distance from point O to ab

（1）∵OA=OB=50，AB=50，
The △ OAB is an equilateral triangle,
∴∠AOB=60°；
(2) OC ⊥ AB at point C through point o,
Then AC = BC = 1
2AB=25，
In RT △ OAC, OC=
OA2−AC2=25
3．
That is, the distance from point O to AB is 25
3．

As shown in the figure, in ⊙ o with radius of 50, the length of chord AB is 50, (1) Find the degree of ∠ AOB; (2) Find the distance from point O to ab

（1）∵OA=OB=50，AB=50，
The △ OAB is an equilateral triangle,
∴∠AOB=60°；
(2) OC ⊥ AB at point C through point o,
Then AC = BC = 1
2AB=25，
In RT △ OAC, OC=
OA2−AC2=25
3．
That is, the distance from point O to AB is 25
3．

If the arc length of the central angle of 1 arc is equal to 2, then the chord length of this central angle is equal to 06 Nanjing

If the arc length C of the central angle of a = 1 radian is 2, then the chord length of the central angle of the circle is l?
The arc radius is r
R=C/A=2/1=2
A = 1 radian = 1 * 180 / pi = 57.3 degrees
L=2*R*SIN(A/2)
=2*2*SIN(57.3/2)
=1.918

If the angle to the center of the arc is the length of the arc with respect to the center of the circle? If the chord length of the center angle of 1 arc is 2, then the arc length of the center angle is? The answer is 1 / sin 0.5

The key of this problem is to ask for the radius of the circle, and make a vertical line to the chord through the center of the circle. Then a right triangle can be constructed. The right angle side of the right triangle is 1, and the center angle of the right angle is 0.5 radian. Then, according to the arc length formula, the radius of the circle is 1 / sin 0.5

If the chord length of the central angle of a circle of 1 radian is 2, then the arc length of the central angle of the circle is

Let the radius of the circle be r
Make a vertical line of string through the center of a circle
It can be seen from the geometric relationship
sin(1/2) = 1/r
r = 1/sin(1/2)
So arc length = 1 * r = 1 / sin (1 / 2)

Given that the chord length of the center angle of 2 radians is 2, then the arc length of the center angle of the circle is () A. 2 B. sin2 C. 2 sin1 D. 2sin1

Connecting the center of a circle and the midpoint of a chord, a right triangle is formed by the distance between chord centers, half of the chord length, and radius. The half chord length is 1, and the center angle of the circle it is facing is also 1
So the radius is 1
sin1
The arc length to which the central angle of the circle corresponds is 2 × 1
sin1=2
sin1
Therefore, C is selected

If the circumference of a fan with radius R is equal to the length of the semicircle where the arc is located, what radians is the central angle of the sector? What's the temperature? What is the area of the sector?

Let the center angle of the sector be θ rad, because the arc length of the sector is R θ,
So the circumference of the sector is 2R + R θ
According to the meaning of the question: 2R + R θ = π R, the solution is θ = π - 2rad
It is converted into angle system as θ = π - 2rad = (π − 2) × 180 degrees
π≈65°19，
Its area is: S = 1
2r2θ＝1
2(π−2)r2

If the circumference of a fan with radius R is equal to the length of the semicircle where the arc is located, what radians is the central angle of the sector? What's the temperature? What is the area of the sector?

Let the center angle of the sector be θ rad, because the arc length of the sector is R θ,
So the circumference of the sector is 2R + R θ
According to the meaning of the question: 2R + R θ = π R, the solution is θ = π - 2rad
It is converted into angle system as θ = π - 2rad = (π − 2) × 180 degrees
π≈65°19，
Its area is: S = 1
2r2θ＝1
2(π−2)r2