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CIRCLES

CIRCLES. Unit 9; Chapter 10. Tangents to Circles lesson 10.1. California State Standards. Lesson Goals. Identify lines and segments in circles. Give the equation for a tangent line on the coordinate plane. Recognize tangent and concentric circles. 7: Prove and Use theorems

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CIRCLES

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  1. CIRCLES Unit 9; Chapter 10

  2. Tangents to Circles lesson 10.1 California State Standards Lesson Goals Identify lines and segments in circles. Give the equation for a tangent line on the coordinate plane. Recognize tangent and concentric circles. 7: Prove and Use theorems involving properties of circles. 21: Prove and Solve relationships among chords, secants and tangents. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

  3. definitions • Circle • The set of all points in a plane that are equidistant from a given point. • Center • The 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.

  4. P definitions • Circle • The set of all points in a plane that are equidistant from a given point. • Center • The 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

  5. definitions • Congruent Circles • Circles with the same radius • Diameter • A line segment with endpoints on the circle that contains the center of the circle. • The distance across a circle through the center. • 2r = d

  6. definitions Y • Congruent Circles • Circles with the same radius • Diameter • A line segment with endpoints on the circle • that contains the center of the circle. • The distance across a circle through the center. • 2r = d P C R • 2r = d X

  7. definitions • Chord • 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.

  8. T U definitions • Chord • 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. B C A F G

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

  10. definition • Tangent Circles • Coplanar circles that intersect in exactly one point. internally tangent circles

  11. definition • Tangent Circles • Coplanar circles that intersect in exactly one point. externally tangent circles

  12. definition • Concentric Circles • Coplanar circles with a common center.

  13. definition • Common Tangent • A line or segment that is tangent to two coplanar circles • Common Internal Tangent crosses between the circles • Common External Tangent stays along the edges of the circles

  14. definition Common Internal Tangent • Common Tangent • A line or segment that is tangent to two • coplanar circles • Common Internal Tangent crosses between the circles • Common External Tangent stays along the edges of the circles Common External Tangent

  15. example Is the common tangent internal or external? C D T external

  16. example Describe each segment and line H tangent diameter E B C G chord F radius I A secant D Point of tangency radius

  17. interior definitions • Interior of a Circle • The set of points inside the circle • Exterior of a Circle • The set of points outside the circle. exterior

  18. example What are the coordinates of each center? y A B x What is the radius of each circle?

  19. example Describe the intersection of the two circles. y A B x

  20. example Describe the common tangents of the circles. y A B x

  21. example What are the coordinates of each center? y What is the radius of each circle? Describe any common tangents. A B x

  22. Today’s Assignment • p. 599: 10 – 16 e, 18 – 35 Tribe Pride always my best effort.

  23. 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. #26 - 28 Tell whether the tangent(s) are internal or external Match the notation with the term that best describes it. #29 - 31 Copy the diagram. Tell how many common tangents the circles have. Then sketch the tangents.

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