Arcs

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K-12: Materials at high school level.



Definition and Examples

An arc is a segment of a circle. You will have seen an arc if you have ever seen rainbow or a crescent moon. Below is also a view of the earth rising as seen from the moon. Astronauts shot this picture.

Arc en ciel 2006.JPG Apollo 15 Earthrise.jpg
A rainbow is an arc. The Earth rising as seen from the moon also forms an arc.

Using Chords to Reconstruct the Circle

If we are given an arc (only part of a circle) we can still figure out how large the whole circle would have been.

For instance, imagine that you are an archaeologist and you are on a dig somewhere and find a piece of a very old dinner plate. This plate is very old so you're lucky to have even found this small piece of it.

Thinking of the plate in terms of circles, we would not have the whole circle. We would only have an arc, which would be a piece of the entire circle. We can figure out the center of the circle by using the chords as we described in the Circles section. This means we could figure out the radius and the diameter of the circle.

Thinking about the plate, this means we would be able to figure out how big the original dinner plate was.

Remember that we would draw two chords. To find the center of the circle we draw the lines that cut the chords in half and are perpendicular to the chord. The intersection of the two lines will be the center of the plate.

Broken-plate.svg Broken-center.svg
A piece of a dinner plate. The location of the center of the plate


The lines we used are called perpendicular bisectors. Perpendicular just means that they meet the segment at a 90 degree angle. Bisector means that they bisect the line segment. In other words divide it in two equal parts.