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Circles

Circles

Arcs

Central angles give rise to another concept that we call: the arc. (Not ark, as in Raiders of the Lost Ark.) More like Noah's ark…but only slightly.

It's hard to define what arcs are formally. Bowties and ball gowns really don't do it for us, anyway. However, we can describe them fairly well like this: an arc is a segment of a circle. Like a line segment, every arc has two endpoints.

Notice that points A and B define two arcs at the same time—there is the arc that directly connects A and B (arc 1, in the figure), and there is the arc that connects A and B by way of point C (arc 2, in the figure).

Every arc has a buddy, just as every central angle has a buddy. To distinguish each arc from its buddy, we usually add points to our figure. In the figure above, we would call arc 2 "arc ACB."

See? Just like the animals on Noah's ark, they come in pairs.

Buddy arcs complete each other just as central angles do. They even hold hands at their endpoints. If that's too mushy-gushy, imagine them shaking hands instead, like esteemed businessmen.

For any arc with two distinct endpoints, we can draw a central angle by drawing two rays, each starting at the center of the circle and going through one of the endpoints. We say that such an angle intercepts that arc, or that the arc subtends that angle. Likewise, any central angle intercepts an arc. Below, ∠AOB intercepts arc AB.

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