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

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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

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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

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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

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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.

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

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Theorem 10.3 P T S R

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Example D 45 43 11 E C

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Example D 14 28 r E r

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Example C A X²-4 21 B D

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