To solve geometry problems involving circles, you'll need to know some basic vocabulary--terms that are likely to show up in any mathematical discussions of the shape. As you study the slides below, add the definitions and diagrams to your notebook. You'll need to be able to recognize these parts throughout this lesson and in other lessons as well.
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A circle is a set of points that are equidistant from a given point, called the center. A circle with center A is called "circle A", or ⊙A. Which of these diagrams is a circle? The circle is the curved "line" shown in red. The shaded area in the diagrams is the area of the circle or ellipse.
A circle's center is a point that is equidistant from all points on the circle. Which diagram shows the center of the circle? The center of a circle is the point that is equidistant from all points on the circle. The center must be marked in order to talk about it.
A radius is a segment with the circle's center as one endpoint and a point on the circle itself as the other endpoint. Which segments in this diagram are radii of the circle? The red segment \(\small\mathsf{ \overline {PB}}\) and the blue segment \(\small\mathsf{ \overline {PA}}\) are radii because one endpoint of each segment is on the circle and the other is the center of the circle.
The diameter of a circle is a segment that goes through the center of the circle and has both endpoints on the circle. Which segment in the following diagram is a diameter of ⊙P? \(\small\mathsf{ \overline {AB}}\) is a diameter of ⊙P.
A chord is a segment with endpoints on a circle. Which segment(s) in the diagram above are chord(s)? \(\small\mathsf{ \overline {CD}}\), \(\small\mathsf{ \overline {EG}}\), and \(\small\mathsf{ \overline {AB}}\) are chords. \(\small\mathsf{ \overline {AB}}\) is a special chord. It is a chord because it is a segment whose endpoints are on the circle. It also goes through the center of the circle; therefore, it is a diameter.
A secant is a line that intersects a circle in two points. Can you identify the diagram that shows a secant? In the left diagram, \(\small\mathsf{ \overleftrightarrow{AB} }\) is a secant. \(\small\mathsf{ \overleftrightarrow{AB} }\) is a line that intersects the circle in two points. In the middle diagram, \(\small\mathsf{ \overleftrightarrow{XY} }\) intersects the circle in just one point and in the last diagram, \(\small\mathsf{ \overline {AB}}\) is a segment, not a line.
A tangent is a line in the plane of a circle that intersects the circle in exactly one point. Which diagram shows a tangent? \(\small\mathsf{ \overleftrightarrow{XY} }\) is a tangent because it intersects the circle in exactly one point.
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