CIRCLES Unit 10

Tangents to Circles lesson 10.1 California State Standards Lesson Goals 7: Prove and Use theorems involving properties of circles. 21: Prove and Solve relationships among chords, secants and tangents. Identify and label lines and segments in circles by using your textbook. State the Congruent Tangents Theorem in your own words. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

definitions Circle Radius The set of all points in a plane that are equidistant from a given point. A circle is named its by center. Radius The distance from the center to a point on the circle. A segment whose endpoints are the center of the circle and a point on the circle.

the plural of radius is radii definitions P Circle The set of all points in a plane that are equidistant from a given point. Radius A line segment with the center as one endpoint and a point on the circle as the other endpoint. The distance from the center to a point on the circle. C the plural of radius is radii

definitions 2r = d Congruent Circles Diameter Circles with the same radius Diameter The distance across a circle through the center. A segment that passes through the center of the circle and whose endpoints are on the circle. 2r = d

definitions Chord Secant Tangent A segment whose endpoints are on the circle. A diameter is a “specialized” chord. Secant A line that intersects a circle in two points. A chord is part of a secant. Tangent A line that intersects a circle in exactly one point. The circle and line must lie in the same plane.

Draw and label the following parts of the circle: (make sure none of the parts of the circle overlap)   Center_______________ Point of Tangency __________ Chord_______________ Radius_______________ Secant______________ Diameter_____________ Tangent_____________

Identify each line or segment point of tangency A secant chord Q radius tangent diameter radius P C X radius chord B Identify each line or segment

definition Concentric Circles Coplanar circles with a common center.

theorem t Tangent-Radius A line is tangent to a circle, if and only if it is perpendicular to the radius drawn to the point of tangency. P t C

example C c a b T A

theorem Congruent Tangents If two segments from the same exterior point are tangent to a circle, then the segments are congruent. P S C Q

example D x2 – 4 C A 21 B

Today’s Assignment Tribe Pride p. 599: 10 – 16 e, 17 – 25, 36, 38, 46 – 48 Tribe Pride always my best effort.

Match the notation with the term that best describes it. 10. The diameter of a circle is 6.7 inches. Find the radius. 12. The diameter of a circle is 8 cm. Find the radius. 14. The radius of a circle is 62 ft. Find the diameter. 16. The radius of a circle is 4.4 cm. Find the diameter. Match the notation with the term that best describes it.