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Download Circles! - Waukee Community School District Blogs
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! Name:!_______________________________________! ! Circles!Packet:! Word! Definition! Radius! Segment!with!endpoints!at!the!center! and!on!the!circle.! Visual! ! ! ! ! ! Chord! Segment!with!endpoints!on!the!circle! ! ! ! ! ! Diameter! A!chord!that!passes!through!the!center! ! and!is!made!up!of!collinear!radii! ! ! ! ! Concentric!Circles! Coplanar!circles!that!have!the!same! ! center! ! ! ! ! Circumference! Distance!around!the!circle! ! ! ! ! ! Central!Angle! ! ! ! ! ! ! Sum!of!Central! The!sum!of!the!measures!of!the!central! ! Angles! angles!of!a!circle!with!no!interior! ! points!in!common!is!360.! ! ! ! Arc! Portion!of!a!circle!defined!by!two! ! endpoints! ! ! ! ! Minor!arc! Shortest!arc!connection!two!endpoints! ! on!a!circle! ! ! ! ! Major!arc! Longest!arc!connecting!two!endpoints! ! on!a!circle! ! ! Semicircle! Arc!with!endpoints!that!lie!on!a! ! diameter! ! ! ! ! Arc!length! Distance!between!the!endpoints!along! ! an!arc!measured!in!linear!units! ! ! ! ! Inscribed!angle! Has!a!vertex!on!a!circle!and!sides!that! ! contain!chords!of!the!circle! ! ! ! ! Intercepted!arc! Has!endpoints!on!the!sides!of!an! ! inscribed!angle!and!lies!in!the!interior! ! of!the!inscribed!angle.! ! ! ! Tangent! Line!in!the!same!plane!as!a!circle!that! ! intersects!the!circle!in!exactly!one! ! point!(point!of!tangency)! ! ! ! Common!Tangent! Line,!ray!or!segment!that!is!tangent!to! ! two!circles!in!the!same!plane! ! ! ! ! Secant! Line!that!intersects!a!circle!in!exactly! ! two!points! ! ! ! ! Secant!segment! Segment!of!a!secant!line!that!has! ! ! exactly!one!endpoint!on!the!circle.! ! ! ! ! External!secant! Secant!segment!that!lies!in!the!exterior! ! segment! of!the!circle! ! ! ! ! Tangent!Segment! Segment!of!a!tangent!with!one! ! endpoint!on!the!circle! ! ! ! ! ! ! ! ! ! Theorem! 10.3! 10.4! 10.5! 10.6!!!Inscribed! Angle!Theorem! 10.7! 10.8! 10.9! 10.10! ! ! ! Words! If!a!diameter!(or!radius)!of!a!circle!is! perpendicular!to!a!chord,!then!it! bisects!the!chord!and!its!arc! ! ! Visual! ! ! ! ! ! ! The!perpendicular!bisector!of!a!chord! ! is!a!diameter!(or!radius)!of!the!circle.! ! ! ! ! ! In!the!same!circle!or!in!congruent! ! circles,!two!chords!are!congruent!if! ! and!only!if!they!are!equidistance!from! ! the!center! ! ! ! If!an!angle!is!inscribed!in!a!circle,!then! ! the!measure!of!the!angle!equals!one! ! half!the!measure!of!its!intercepted!arc.! ! ! ! ! If!two!inscribed!angles!of!a!circle! ! intercept!the!same!arc!or!congruent! ! arcs,!then!the!angles!are!congruent! ! ! ! ! An!inscribed!angle!of!a!triangle! ! intercepts!a!diameter!or!semicircle!if! ! and!only!if!the!angle!is!a!right!angle! ! ! ! ! If!a!quadrilateral!is!inscribed!in!a! ! circle,!then!its!opposite!angles!are! ! supplementary! ! ! ! ! In!a!plane,!a!line!is!tangent!to!a!circle!if! ! and!only!if!it!is!perpendicular!to!a! ! radius!drawn!to!the!point!of!tangency.! ! ! ! ! ! ! ! 10.11! ! If!two!segments!from!the!same! exterior!point!are!tangent!to!a!circle,!! then!they!are!congruent! ! ! ! ! ! ! ! ! 10.12! If!two!secants!or!chords!intersect!in! ! the!interior!of!a!circle,!then!the! ! measure!of!an!angle!formed!is!one!half! ! the!sum!of!the!measure!of!the!arcs! ! intercepted!by!the!angle!and!its! ! vertical!angle! ! ! 10.13!! If!a!secant!and!a!tangent!intersect!at! ! the!point!of!tangency,!then!the! ! measure!of!each!angle!formed!is!one! ! half!the!measure!of!its!intercepted!arc! ! ! ! ! 10.14! If!two!secants,!a!secant!and!a!tangent,! ! or!two!tangents!intersect!in!the! ! exterior!of!a!circle,!then!the!measure!of! ! the!angle!formed!is!one!half!the! ! difference!of!the!measures!of! ! intercepted!arcs! ! ! 10.15!Segments! If!two!chords!intersect!in!a!circle,!then! ! of!Chords! the!products!of!the!lengths!of!the! ! Theorem! chord!segments!are!equal! ! ! ! ! ! ! 10.16!Secant! If!two!secants!intersect!in!the!exterior! ! Segments! of!a!circle,!then!the!product!of!the! Theorem! measures!of!one!secant!segment!and! its!external!secant!segment!is!equal!to! the!product!of!the!measures!of!the! other!secant!and!its!external!secant! segment! 10.17! If!a!tangent!and!a!secant!intersect!in! ! the!exterior!of!a!circle,!then!the!square! ! of!the!measure!of!the!tangent!is!equal! ! to!the!product!of!the!measures!of!the! ! secant!and!its!external!secant!segment.! ! ! ! Equation!of!a!Circle:! ! ! !
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