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In ⊙ o with radius 1, if chord AB = 1, then The length of AB is () A. π Six B. π Four C. π Three D. π Two
As shown in the figure, make OC ⊥ ab,
According to the vertical diameter theorem, BC = 1
Two
∵ chord AB = 1,
∴sin∠COB=1
Two
∴∠COB=30°
∴∠AOB=60°
Qi
Length of AB = 60 π
180=π
3．
Therefore, C
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 To have a problem-solving process, thank you
Center angle a = 45 * 2 = 90 degrees
Arc length = 2 * pi * r * 90 / 360 = 47 * pi
2*PI*R/4=47*PI
R/2=47
R=94cm
If a chord divides a circle into two 1:3 arcs, the angle of the circle to which the chord is directed is
A string divides the circle into two 1:3 arcs,
Then the circle angle of the chord is 135 ° or 45 °
A chord of a circle divides the circumference into two arcs with degree ratio of 1:2. If the radius of the circle is 4, find the length of the two arcs and the circumference angle of the inferior arc
If a chord of a circle divides the circumference into two arcs with degree ratio of 1:2, the ratio of the center angle of the two arc lengths is 1:2, and the ratio of the circumferential angle of the two arc lengths is 1:2, the center angle of the superior arc is 360 * (1 / 3) = 120 degree, the circumference angle is 60 degrees, the center angle of the inferior arc is 360 * (2 / 3) = 240 degrees, the circumference angle is 120 degrees, the length of the two arcs is the length of the superior arc: (
The ratio of a chord dividing a circle into two arcs is 1:2
If it is the circumference angle of the small arc, then it is 60 degrees. 2. If it is the circumference angle of the big arc, then it is 120 degrees. The ratio of the center angles of the two arcs is 1:2
The radius of circle O is 2 and chord AB is 2?
Connect the center of the circle and two points a and B with radius of 2 and ab = 2
So it's an equilateral triangle, so the angle AOB is 60 degrees
The circumference angle is 30 degrees
It is known that in ⊙ o, the distance between the center of circle O and chord AB is equal to half of the radius, then the angle degree of circle center of inferior arc is () A. 45° B. 60° C. 90 D. 120°
∵OA=OB，OD⊥AB，
ν, i.e., AOD ∠,
In RT △ AOD, OD = 1
2OA，
∴∠OAD=30°，∠AOD=60°，
Then ∠ AOB = 2 ∠ AOD = 120 °
Therefore, D
In 0o, the chord center distance of chord AB is equal to half of the chord length, and the minor arc length of the chord is 4 π cm. Try to find the radius of 0o
In 0o, the chord center distance h of chord AB is equal to half of the chord length L, and the minor arc length of the chord is 4 π cm. Try to find the radius r? Of 0 o?
The center angle of the arc is a
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=(L/2)/2+L^2/(8*(L/2))
=L/4+L^2/(4*L)
=L/4+L/4
=L/2
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((L/2)/(L/2))
=180 degrees
=180*PI/180
=PI radian
C=A*R=PI*R=4*PI
R=4cm
In the circle O with radius of 2cm, if the chord center distance of chord AB is 1cm, then the degree of inferior arc AB is
If the chord center distance is 1cm and the radius is 2cm, the angle between chord and radius is 30 degrees, and half of the center angle is 60 degrees. Therefore, the center angle is 120 degrees, so the degree of inferior arc AB is 120 degrees
If the length of the chord center distance of a string is equal to 1 / 4 of the diameter of its circle, what is the degree of inferior arc of the string?
For example, if AB is the diameter of circle O, BC is the chord of circle O, and the chord center distance of BC is OE = AB / 4, the angle BOC (actually the degree of minor arc) can be obtained
In the RT triangle BOE, OB = AB / 2, and OE = AB / 4, then OE = ob / 2, so the angle B = 30 degrees, so the angle EOB = 60 degrees,
The angle BOC = 120 degrees, that is, inferior arc BC = 120 degrees
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