There is a chord in a circle with radius 1. If its length is root 3, then what is the degree of circumference angle of this string Can we do it without trigonometric functions?

According to the known, three chords with the length of root 3 are connected to form a circle inscribed equilateral triangle, and the degrees of the two circumference angles are 60 and 120

It is known that in a circle O with a radius of 3cm, the length of the chord AB is three root signs 3cm. The readings of the center angle and the circumference angle of the chord are obtained

As the perpendicular line od of a string, then the AOD of the right triangle is 3, and ad is 3 / 2. According to the Pythagorean theorem, OD = 3 / 2 and angle AOD = 60 degrees can be obtained
AOB = 2aod = 120 degrees
Circle angle = half of center angle = 60 degrees

In a circle with a radius of five centimeters, there is a string with a length of five root sign three. How about the circumference angle of this string?

The center angle a of the circle to which this string is opposite
cosA=(5*5+5*5-5*5*3)/(2*5*5)=-1/2;
A = 120 ° and the circumferential angle of this chord is 60 ° respectively

What is the diameter of a circle if the circumference angle of a 5cm long string is 45 degrees? 10cm 5 times root number 2cm 5cm cannot be calculated

As shown in the figure, the radius of ⊙ o is 1, AB is a chord of ⊙ o, and ab is a chord of ⊙ o= 3, then the degree of the circumference angle of the chord AB is______ .

As shown in the figure,
If OA and ob are connected, if O is used as of ⊥ AB, then AF = 1
2AB，∠AOF=1
2∠AOB，
∵OA=1，AB=
3，
∴AF=1
2AB=1
2 x
3=
Three
2，
∴sin∠AOF=AF
OA=
Three
Two
1=
Three
2，
∴∠AOF=60°，
∴∠AOB=2∠AOF=120°，
ν the circumference angle of arc AB = ∠ AOF = 1
2∠AOB=1
2×120°=60°，
Take point E on inferior arc AB to connect AE and EB,
∴∠AEB=180°-60°=120°．
So the answer is: 60 ° or 120 °

In the circle O with radius 1, if chord AB = 1, the length of arc AB is ()

The triangle Ab0 is an equilateral triangle, so the angle AOB is 60 ° and the long time of inferior arc AB is 1 / 6 × 2 π = π / 3. The long time of superior arc AB is 2 π - π / 3 = 5 π / 3

In circle O, the chord center distance of chord AB is equal to half of the chord length, and the arc length of the chord is 47 π cm. Calculate the radius of circle o

OC ⊥ AB to C through o,
Then AC = BC = 1 / 2Ab,
∵OC=1/2AB,
ν Δ AOC is an isosceles right triangle,
∴∠AOC=45°,
∴∠AOB=90°,
The inferior arc AB = 1 / 4 * 2 π r = 47 π,
R=94㎝.

In a circle with a radius of 5cm, how many cm is the chord length of a string when the chord center distance is 4cm

Chord, radius and chord center distance can form two identical right triangles,
According to the Pythagorean theorem,
Half of the string L / 2 = √ (r? - D?) = √ (5? - 4?) = √ 9 = 3cm,
Therefore, the chord length is L = 2 * 3 = 6cm

In a circle with a diameter of 10 cm, if the length of chord AB is 8 cm, then its chord center distance is______ cm．

∵ the diameter is 10 cm,
∴OA=5cm，
∵OC⊥AB，
∴AC=1
2AB=4cm，
In RT △ OAC, according to Pythagorean theorem, the
OC=
OA2−AC2=
52−42=3cm．
The chord center distance is 3cm

If a chord of a circle divides the circle into two arcs with a degree ratio of 1:4, the circumference angle of the inferior arc is equal to?

360°×1/5=72°
The circle angle of inferior arc is equal to 36 degrees

There is a chord in a circle with radius 1. If its length is root 3, then what is the degree of circumference angle of this string Can we do it without trigonometric functions?