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Tangents to circles 10.1 pg595

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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.

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

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

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

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

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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

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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

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Tangent Circles Concentric Circles

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Common Internal Tangent Common External Tangent

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Example Common internal or external tangent? external

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

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

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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

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Example Is segment CE tangent to circle D? Explain D E C 11 45 43 11 2 +43 2 =45 2 121+1849=2025 1970=2050 NO

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Example solve for the radius, r A B C r r 28ft 14ft r 2 +28 2 =(r+14) 2 r 2 + 784=r 2 + 28r+196 784=28r+196 588=28r 21=r

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

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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 2 +8 44 x 2 +8=44 x 2 =36 X=6, -6

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