2 A circle is the set of points in a plane that are equal distance, the radius (r), from a given point, the center, which is also in the plane.Twice the radius of a circle is called the diameter of the circle.r
3 The center of the circle is point A. A circle is named by its center The center of the circle is point A. A circle is named by its center. This circle is called circle A Another definition of a radius of a circle is a segment whose endpoints are the center of the circle and a point on the circle. In circle A segment AB is a radius.AB
4 Chord of a CircleA chord of a circle is a segment whose endpoints are on the circle.CSegment CB is a chord of circle A.AB
5 A diameter of a circle is a segment that passes through the center of the circle and whose endpoints are on the circle.Segment DB is a diameter of circle A.DAB
6 Tangent of a CircleA tangent of a circle is a line that intersects the circle in exactly one point.AELine BE is a tangent of circle A.BPoint B is the point of tangency.
7 Secant of a CircleA secant of a circle is a line, a ray, or a segment that contains a chord of a circle.ALine BC is a secant of circle A.CB
8 Example 1Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C.
20 1st Tangent TheoremA line, a ray, or a segment is tangent to a circle if and only if it is in the same plane as the circle and is perpendicular to a radius of the circle at the point of intersection.
21 Line BE is a tangent of circle A if and only if it is perpendicular to radius AB at point B.
22 Example 4In the diagram, segment AB is a radius of circle A. Is segment BC tangent to circle A? Explain. Segment BC is tangent to circle A if segment BC radius AB at pt. B.Therefore Δ ABC is not a right Δ and segmentBC is not perpendicular to radius AB.
23 Example 5In the diagram, S is a point of tangency. Find the radius r of circle T.
24 2nd Tangent TheoremTangent segments from a common external point are congruent.