Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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Part of a circle between two endpoints is called an **arc**. The **measure of an arc** is the angle made from lines drawn from the center of the circle to the endpoints of the arc.

If the measure of the arc is less than 180°, it is a **minor arc**. If the measure of the arc is exactly 180°, it is a **semicircle**. If the measure of the arc is greater than 180°, it is a **major arc**.

A **chord** is a line segment whose endpoints are on the circle, but it is not on the circle itself. Instead of being curved like an arc, a chord is a straight line. A **tangent** is a line that touches only one point on the circle.

If you take just part of a circle, that’s going to be considered an arc. So here I’ve drawn arc ab which I can write as ab with an arc over it, so an arc is the continous part of a circle between two end points. So if you’d pick two points on a circle, an arc is all the points that are in between those two endpoints and we measure that arc by measuring the central angle. Well the central angle as it probably sounds is centered at the centre of the circle, so if I found the center of this circle containing that arc and I drew in radii to the endpoints, this would be mu centre angle. So the vertex of a central angle is at the centre of the circle.

Now let’s say if measure x, a measure of this arc. If x is less than 180 degrees then we call that a minor arc. If x is equal to exactly 180 degrees, half a circle, we call that a semicircle, and last if x is greater than 180 degrees we call that a major arc. So if you take just part of a circle, it’s going to be considered an arc and we can differentiate different types of them by the degree in measure.

Now two other key things about circles are tangents and chords. So a chord is a line segment whose endpoints are on the circle and it connects those two points and it does not follow the circle, otherwise that would be the arc. So this right here is a chord because its endpoints are on the circle and if it passes through the center then it is considered a diameter. Now the last key term is a tangent and what a tangent is; let’s say you picked a point on that circle, anywhere on that circle and you drew a line that intersected that tangent exactly once or if you drew a line that intersected that circle exactly once, this is considered a tangent. So a tangent by definition is a line, a line segment or a ray that will intersect a circle in exactly one point. Notice that if I shift this up just a tinny bit we would have part of a chord, because it would pass through the circle and we would have two point of intersection. Now this point here where your line, that’s tangent, intersects your circle is called the point of tangency.

So this is all the key vocabulary that you need to know about circles.