Lines That Intersect Circles

Transcription

1 LESSON 11-1 Lines That Intersect Circles Lesson Objectives (p. 746): Vocabulary 1. Interior of a circle (p. 746): 2. Exterior of a circle (p. 746): 3. Chord (p. 746): 4. Secant (p. 746): 5. Tangent of a circle (p. 746): 6. Point of tangency (p. 746): 7. Congruent circles (p. 747): 8. Concentric circles (p. 747): 9. Tangent circles (p. 747): 10. Common tangent (p. 748): 234 Geometry

2 LESSON 11-1 Lines That Intersect Circles Lesson Objectives (p. 746): identify tangents, secants, and chords; use properties of tangents to solve problems. Vocabulary 1. Interior of a circle (p. 746): the set of all points inside the circle. 2. Exterior of a circle (p. 746): the set of all points outside the circle. 3. Chord (p. 746): a segment whose endpoints lie on a circle. 4. Secant (p. 746): a line that intersects a circle at two points. 5. Tangent of a circle (p. 746): a line in the same plane as the circle that intersects it at exactly one point. 6. Point of tangency (p. 746): the point where the tangent and a circle intersect. 7. Congruent circles (p. 747): circles that have congruent radii. 8. Concentric circles (p. 747): coplanar circles with the same center. 9. Tangent circles (p. 747): coplanar circles that intersect at exactly one point. 10. Common tangent (p. 748): a line that is tangent to two circles. 234 Geometry

3 Key Concepts 11. Lines and Segments That Intersect Circles (p. 746): TERM CHORD DIAGRAM SECANT TANGENT POINT OF TANGENCY 12. Pairs of Circles (p. 747): TERM CONGRUENT CIRCLES DIAGRAM CONCENTRIC CIRCLES TANGENT CIRCLES 235 Geometry

4 Key Concepts 11. Lines and Segments That Intersect Circles (p. 746): TERM CHORD A chord is a segment whose endpoints lie on a circle. SECANT A secant is a line that intersects a circle at two points. TANGENT A tangent is a line that intersects a circle at exactly one point. POINT OF TANGENCY The point of tangency is the point where the tangent and a circle intersect. DIAGRAM A Tangent Chord B Secant m C Point of tangency 12. Pairs of Circles (p. 747): TERM CONGRUENT CIRCLES Two circles are congruent circles if and only if they have congruent radii. CONCENTRIC CIRCLES Concentric circles are coplanar circles with the same center. TANGENT CIRCLES Two coplanar circles that intersect at exactly one point are called tangent circles. DIAGRAM A C B D A B if A C B D. A C B D if A B. internally tangent circles Externally tangent circles 235 Geometry

5 13. Theorems (p. 748): THEOREM HYPOTHESIS CONCLUSION Theorem (p. 749): THEOREM HYPOTHESIS CONCLUSION Geometry

6 13. Theorems (p. 748): THEOREM HYPOTHESIS CONCLUSION If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. (line tangent to line to radius) If a line is perpendicular to a radius of a circle at a point on the circle, then the line is tangent to the circle. (line to radius line tangent to ) A B is tangent to A C D m m is to C D at D. AB m is tangent to C 14. Theorem (p. 749): THEOREM HYPOTHESIS CONCLUSION If two segments are tangent to a circle, from the same external point, then the segments are congruent. (2 segs. tangent to from same ext. pt. segs ) P B C AB and AC are tangent to P. A AB AC 236 Geometry

7 15. Get Organized In each box, write a definition and draw a sketch. (p. 750). Congruent Concentric Circles Internally tangent Externally tangent 237 Geometry

8 15. Get Organized In each box, write a definition and draw a sketch. (p. 750). Congruent s with radii Concentric s with the same center Circles intersect at exactly 1 pt. Internally tangent intersect at exactly 1 pt. Externally tangent 237 Geometry