# 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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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 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.

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

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

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

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

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

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

Tangent Circles Concentric Circles

Common Internal Tangent Common External Tangent

Example Common internal or external tangent? external

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

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

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

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

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

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

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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