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The answer is easier if angles are measured in radians. At the end, you'll get a conversion from radians to degrees.
You are given a circle with diameter d, and a chord that subtends an arc of length x. Let c be the length of the chord and write r = d/2 for the radius of the circle.
The arc subtends an angle of y = x/r radians at the centre of the circle.
(If you draw a chord and the perpendicular from the centre of the circle to the midpoint of the chord, the following trigonometry is easier to understand).
sin(y) = (c/2)/r where c is the length of the chord.
so sin(y) = c/2r
and so c = 2r*sin(y) = d*sin(y) = d*sin(x/r) = d*sin(x/2d)
Everything on the right hand side is known and so c is easily calculated.
Radians-degrees
A whole circle is 360 degrees of 2*pi radians so 1 radian = 180/pi degrees. Writing 180/pi each time is tedious and also, higher maths is all in radians anyway, so I tend to avoid working with degrees. If you are using this on a calculator, make sure the angles are being measured in radians. The default units for angles in Excel is radians.
What else can I help you with?
How do you find radius of a circle if cord length is given?
The longest chord in a circle is its diameter and halve of this is its radius.
How do you find the chord of a circle?
all you have to do is find a line with two endpoints on the circle also a diameter is the longest chord on a circle that runs through the middle of the circle.
How do you find the radius of a circle when the diameter is given?
Divide the diameter by 2.
How do you find the radius of a circle if you know the length of a chord is 4 cm length?
Unless the chord is the diameter, there is no way to measure the radius of the circle. This is because the radius is in no way dependent on chord length since circles have infinite amount of chord lengths.
What is a chord passing through the center of a circle?
a diameter
How do you find radius of a circle if cord length is given?
The longest chord in a circle is its diameter and halve of this is its radius.
How do you find the radius given the chord length?
If you are given a chord length of a circle, unless you are given more information about the chord, you can not determine what the radius of the circle will be. This is because the chord length in a circle can vary from a length of (essentially) 0, up to a length of double the radius (the diameter). The best you can say about the radius if given the chord length, is that the length of the radius is at least as long has half half the chord length.
How do you find the chord of a circle?
all you have to do is find a line with two endpoints on the circle also a diameter is the longest chord on a circle that runs through the middle of the circle.
How do you find the length of diameter when the center of the circle is unknown?
It'll be the largest chord of the circle.
Where would uu find a chord on a circle?
A chord - is a straight-line joining two points on the circumference. The longest chord is the diameter.
How do you find the DIAMETER if given the circumference OF A CIRCLE?
Diameter of a circle = circumference/pi
How do you find the radius of a circle when the diameter is given?
Divide the diameter by 2.
How does one find the diameter of a circle?
The diameter of a circle is simply twice the radius. It is the length of a chord running thru the center point of the circle. Can also be found by taking the circumference and dividing it by pi.
How do you find the radius of a circle if you know the length of a chord is 4 cm length?
Unless the chord is the diameter, there is no way to measure the radius of the circle. This is because the radius is in no way dependent on chord length since circles have infinite amount of chord lengths.
If the area of a circle is given as 67cm squared find the diameter and then circumference of this circle?
If the area of a circle is given as 67cm squared, the diameter is 9.236 cm and the circumference is 29.02 cm
What is a chord passing through the center of a circle?
a diameter
How do you find a chord of a circle with diameter 26?
There are an infinite number of possible chords in anycircle, regardless of its diameter. A chord is a line segment with its endpoints on the curve (circumference) of the circle. You can draw those all day and never draw the same one twice.
