Chapter 10 Circles Section 10.1 Goal – To identify lines and segments related to circles To use properties of a tangent to a circle

Circle Circle - The set of all points in a plane that are equidistant from a given point called the center “C”. d = 2r If two circles are congruent, then they have the same ___________. r d C

Vocabulary Chord – a segment whose endpoints are points on the circle. Secant – a line that intersects a circle in two points. Tangent – a line that intersects the circle in exactly one point. Diameter – the distance across the circle through the center. Radius – the distance from the center to a point on the circle. Example: Name a chord, secant, tangent, diameter and radius. Q R P T N S V j k

Intersecting Circles In a plane, two circles can intersect in two points, one point, or not points. Two points of intersection One point of intersection (tangent circles) No points of intersection

Common Tangents of Two Circles n B A D C m j k j is a common internal tangent because it intersects the segment that joins the centers of the two circles. m is a common external tangent because it does not intersect the segment that joins the centers of the two circles.

Theorem 10.1 & 10.2 If l is tangent to circle Q at point P, then Q P l

Theorem 10.3 P T S R

Example D E C

Example D r E r

Example C A X²-4 21 B D