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Tangents to circles 10.1 pg595. Definitions Circle- the set of all pts in a plane that are equidistant from a given pt. Center- pt in the middle of the.

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Presentation on theme: "Tangents to circles 10.1 pg595. Definitions Circle- the set of all pts in a plane that are equidistant from a given pt. Center- pt in the middle of the."— Presentation transcript:

1 Tangents to circles 10.1 pg595

2 Definitions Circle- the set of all pts in a plane that are equidistant from a given pt. Center- pt in the middle of the circle Radius- distance from the center of a circle to a pt on the circle Diameter- a chord that passes through the center of a circle.

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

4 Chord Chord- a segment whose end pts are on the circle. A B

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

6 Tangent Tangent- line that intersects a circle in exactly one pt.

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

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 Example Common internal or external tangent? external

12 Last definition Pt of tangency- pt where tangent intersects a circle T Pt T is the pt of tangency

13 Thm 10.1 If a line is tangent to a circle, then it is perpendicular to the radius drawn to the pt of tangency.

14 Thm 10.2 In a plane if a line is perpendicular to a radius of a circle at the endpt that is on the circle, then the line is tangent to the circle

15 Example Is segment CE tangent to circle D? Explain D E C = = =2050 NO

16 Example solve for the radius, r A B C r r 28ft 14ft r =(r+14) 2 r =r r =28r =28r 21=r

17 Thm 10.3 If 2 segs from the same exterior pt are tangent to a circle, then they are .

18 Example segment AB is tangent to circle at pt B. segment AD is tangent to circle c ant pt D. Find the value of X C B D A x x 2 +8=44 x 2 =36 X=6, -6


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