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Use Properties of Tangents

Use Properties of Tangents. Lesson 6.1 Pg 182. Vocabulary. Circle- the set of all pts in a plane that are equidistant from a given pt. called the center of the circle. Radius- segment whose endpoints are the center and any point on the circle

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Use Properties of Tangents

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  1. Use Properties of Tangents Lesson 6.1 Pg 182

  2. Vocabulary • Circle- the set of all pts in a plane that are equidistant from a given pt. called the center of the circle. • Radius- segment whose endpoints are the center and any point on the circle • Diameter- a chord that contains the center of the circle. • Two polygons are similar if corresponding angles are congruent and corresponding side lengths are proportional. ΔABC ΔDEF

  3. P is the center of the circle Segment AB is a diameter B P Segments AP, PB, and PC are radii A C

  4. Chord • Chord- a segment whose endpoints are on the circle. B A

  5. Secant • Secant- a line that intersects a circle in 2 pts B A

  6. Tangent • Tangent- a line in the plane of the circle that intersects the circle in exactly one point, called the point of tangency.

  7. Pt of tangency- pt where tangent intersects a circle Pt T is the pt of tangency T

  8. Exampletell whether the segment is best described as a chord, secant, tangent, diameter or radius • Segment AH • Segment EI • Segment DF • Segment CE H tangent Diameter E Chord B G radius C I F A D

  9. More Definitions • Tangent circles- circles that intersect in one pt • Concentric circles- circles that have a common center but different radii lengths • Common tangent- a line or segment that is tangent to two circles • Common internal tangent- a tangent that intersects the segment that connects the centers of the circles • Common external tangent- does not intersect the segment that connects the centers

  10. Tangent Circles Concentric Circles

  11. Common Internal Tangent Common External Tangent

  12. ExampleCommon internal or external tangent? external

  13. Theorem 6.1 • In a plane, a line is tangent to a circle if and only if it is perpendicular to a radius of the circle at its endpoint on the circle.

  14. ExampleIs segment CE tangent to circle D? Explain E 11 43 D 45 C 112+432=452 121+1849=2025 1970=2050 NO

  15. Examplesolve for the radius, r B 28ft r C A r 14ft r2+282=(r+14)2 r2+ 784=r2+ 28r+196 784=28r+196 588=28r 21=r

  16. Theorem 6.2 • Tangent segments from a common external point are congruent.

  17. Examplesegment AB is tangent to circle C at pt B. segment AD is tangent to circle C at pt D. Find the value of X B x2+8=44 x2+8 x2=36 X=6 C A 44 D

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