Working out the length of an arc in a cirlce question?

Question

Hello,
A chord 26mm is drawn in a circle of 35mm diameter. What are the lengths of arcs into which the circumference is divided?

Im trying to answer the above question, but im finding it very hard to start, i know ive got to find the length of the minor arc and major arc, but im really not sure how to go about it,

Any help would be much appreciated,
Cheers

Answer 1

Since the chord is arbitrary, consider it horizontal. You know the length of the chord, 26 mm; and the diameter of the circle, 35 mm.

If you consider a radius perpendicular to the midpoint of the chord, you can create a right triangle with a horizontal side 13 mm long and a hypotenuse 17.5 mm long. From trig identities you can find appropriate angles.

Once you know the angles subtended by the parts of the original circle, you can turn them into line lengths using the calculated circumference of the circle.

Answer 2

There's probably a simpler way, but the following should work.

You want to find the total angle that the chord spans. So from the center of the circle draw a triangle (lines from center to each point where chord meets circle).

Then divide the triange in half to create two right-angle triangles.

The lines you have drawn will have a length equal to the radius of the circle, and since you know the diameter the radius is diameter divided by 2*pi.

Since you know the length of the chord, half that is the length of the far side of the triangle.

Since you know the lengths of two sides of each right angle triangle, you can figure out the angle (use inverse sine).

Once you know the total angle formed by the two right angle triangles, you figure out what portion of 360 degrees is spanned, and divide the diameter by the same amount. That will be the minor arc and the remainder of the diameter would be the major arc.

Sorry for all the steps!

Answer 3

You can use the cosine law:

a^2 = b^2+c^2-2bc*(cosA) where a = b = 35/2 = 17.5 mm radius and c = 26 mm chord. From the center of the circle, draw two radii that would intersect the circle at the beginning and end of the chord length. All three distances are known but no angles. Use the cosine law to solve for the angles

solving for A = 42.025 degrees
by symmetry B = 42.025 deg and the interior angle is 95.95 deg

since a circle = 360 degrees, 95.95 degrees comprises only .26653 of a full circle. the comcomitant arc length = .26653* the circle circumference = .26653*3.14159*36 = 30.1435 mm

Answer 4

This question is better answered if you actually draw the circle and draw the chord into it. From there, you can look up the formulas. You can find info on
"Circle Calculator", http://www.1728.com/circsect.htm
"Chord (geometry) - Wikipedia", http://en.wikipedia.org/wiki/Chord_%28geometry%29

Good Luck!! Sorry I cant be of real help but I havent had geometry since HS (like 10 years ago!!)

Answer 5

L=R^
Length = radius X delta