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CIRCLES Unit 9; Chapter 10

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

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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.

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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 P the plural of radius is radii

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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. 2 r = d

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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 definitions P C R 2r = d X Y

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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.

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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. definitions C A B F G T U

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

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

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

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definition Concentric Circles Coplanar circles with a common center.

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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

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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 definition C o m m o n I n t e r n a l T a n g e n t Common External Tangent

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

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

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

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example What are the coordinates of each center? What is the radius of each circle? x y AB

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example Describe the intersection of the two circles. x y AB

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example Describe the common tangents of the circles. x y AB

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

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22 Todays Assignment p. 599: 10 16 e, 18 35

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