The chord length is 2000 and the arc length is 2001, find the central angle and radius of the circle

Draw a horizontal line with a string length of 2000, draw a circle with a diameter of 2000 with the middle point of the line, cut off the lower half circumference, click on the arc to make it appear a grip point, which is a small solid box, click the grip point to move up and down and cooperate with the scroll wheel to scale, when the arc length size shows "2001", put it down, it is very easy to find the central angle and radius.

If it is AutoCAD 2010 or later, it is more convenient to use the constraint function to directly constrain the arc length to "2001". I haven't tried it yet, hehe.

Solve inside a triangle.

Let the central angle of the circle be and the radius be r, then we can establish the equation: the angle here is in radians.

r=2001；

rcos(α/2)=2000

These two equations can be solved.

The chord length l=2000, the arc length c=2001, and the central angle a and radius r?

rn+1=(1+(l-2*rn*sin(c/(2*rn)))/(l-c*cos(c/(2*rn)))rn

r0=18000

r1=r2=

r3=r4=

r=a=2*arc sin((l/2)/r)

2*arc sin((2000 2) degrees.

The radius of the circle and the length of the chord are known, and the arc length is found.

Let the radius be r, the length of the string is b, the arc length is hall l, and the central angle of the arc is , then sin( 2)=(b 2) r=b 2r;

Hence =2arcsin(b 2r); So the arc length l=r =2rarcsin(b 2r)

Knowing the half-observed parallel diameter r, arc length c, how to find the chord length l?

The central angle of the arc is a

a=c rradian = (c r)*(180) degrees.

l=2*r*sin(a 2)=2*r*sin((c r)*(180)2)=2*r*sin((c r)*(90 defeat trace)).

Knowing the chord length l, radius r, how to find the central angle a and the arc length c?

a=2*arc sin((l 2) r) degrees=2*(arc sin((l 2) r))*pi 180)rad c=r*a=2*r*(arc sin((l 2) r))*pi 180).

Knowing the arc length c= and the angle a= degrees, find the chord length l?

The radius of the arc is r.

Angle a = degree = radian.

r=c a=m.

l=2*r*sin(a/2)

2*=m. Knowing the arc length c= and radius r=8, find the chord length l?

The central angle of the circle is a.

a=c r=radians = degrees.

l=2*r*sin(a/2)

2*8*sin(=m.)

Answer: First, the radius length can be obtained by dividing the arc length by the radius angle, and then using the cosine theorem, assuming that the radius angle is (known), the radius length is r (calculated), the chord length is x (unknown), and cos = (r 2+r 2-x 2) 2r 2, and the chord length can be found by solving this equation.

Arc length formula. n is the central angle of the circle.

The degree of rock and the number of dispatches, r is the radius.

l=nπr÷180

Known arc length, central angle, radius = 180°l n known circular obscuring central angle, radius, arc length = n r 180° known arc length and radius, central angle = 180°l r

Hope it helps, hope, thank you

The arc length is c = m, the chord length is l = 5 m, and the radius r is how many m?

rn+1=(1+(l-2*rn*sin(c (2*rn)))guess (l-c*cos(c (2*rn)))rn

r0=3r1=

r2=r3=

r4=r5=

r = m.

Knowing the chord length l=9600 arc length c=10010, find the central angle a and the radius r?

rn+1=(1+(l-2*rn*sin(c/(2*rn)))/(l-c*cos(c/(2*rn)))rn

r0=10000

r1=r2=

r3=r=a=2*arc sin((l/2)/r)

2*arc sin((9600 2) = degrees.

Using the trigonometric string, the relationship between the angle and the radius to list one equation, and the second equation using the relationship between the arc length and the angle, only the angle and radius are unknown in the two equations, so they can be solved. One of the things about knowledge is a trigonometric equation.