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6.1 (M2) Use Properties of Tangents

6.1 (M2) Use Properties of Tangents. 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 Chord – A segment whose endpoints are on a circle

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6.1 (M2) Use Properties of Tangents

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  1. 6.1 (M2) Use Properties of Tangents

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

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

  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. 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

  8. 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

  9. Tangent Circles Concentric Circles

  10. Common Internal Tangent Common External Tangent

  11. ExampleCommon internal or external tangent? external

  12. Theorem • 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.

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

  14. 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

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

  16. 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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