ࡱ>  *,)e^rUq` bjbjqPqP 4@::_ RPPPPPPP8,| 5h$Z5\5\5\5\5\5\5$C7h9|5P5PP5(PPZ5Z50PPt2 pn (t13d5051':-':(t2t2':P355 5  dD,PPPPPP  Big Ideas: Chord Definition: A chord is a line segment whose two endpoints lie on a circle.  EMBED Visio.Drawing.6 Chord Distance to Center Theorem Two congruent chords in a circle are equidistant from the center of the circle. Perpendicular to a Chord Theorem The perpendicular from the center of a circle to a chord is the bisector of the chord. Perpendicular Bisector of a Chord Theorem The perpendicular bisector of a chord passes through the center of the circle.Secant Definition: A secant is a line that intersects a circle at exactly two points.  EMBED Visio.Drawing.6  A Major Arc is the larger of the two arcs created by a chord or secant. A Minor Arc is the smaller of the two arcs created by a chord or secant. Tangent Definition: A tangent is a line that intersects a circle at one and only one point.  EMBED Visio.Drawing.6 Tangent Theorem A tangent to a circle is perpendicular to the radius drawn to the point of tangency. Circles and the Measures of Related Angles Note that all of the angles involve the fraction  EMBED Equation.DSMT4  as a multiple of either: 1) the measure of one intercepted arc; or 2) (with external angles) the difference of the measures of two intercepted arcs or 3) (with vertical angles of intersecting chords) the sum of the measures of the two intercepted arcs.Inscribed Angles The measure of an angle inscribed in a circle is one-half the measure of the intercepted arc.  EMBED Visio.Drawing.6  Inscribed Angle Intersecting Same Arc Theorem Inscribed angles that intercept the same arc are congruent. Angles Inscribed in a Semicircle Theorem Angles inscribed in a semicircle are right angles.Angles Formed by 2 Tangents  EMBED Visio.Drawing.6 Angles Formed by 1 Tangent and 1 Chord  EMBED Visio.Drawing.6  Angles Formed by 2 Secants  EMBED Visio.Drawing.6 Angles Formed by 1 Tangent and 1 Secant  EMBED Visio.Drawing.6 Intersecting Chords Theorem The measure of the angle formed by two intersecting chords is equal to one-half the sum of the measures of the two intercepted arcs. (  EMBED Visio.Drawing.6  Measures of the Lengths of Chords, Secants, and TangentsLengths of Inscribed Chords  EMBED Visio.Drawing.6  Lengths of Secant-Tangent Angles  EMBED Visio.Drawing.6  Lengths of Secant-Secant Angles  EMBED Visio.Drawing.6 Tangent Segments Theorem Tangent segments to a circle from a point outside the circle are congruent.  EMBED Visio.Drawing.6  Modeling: Sample Math B Regents Problem A toy truck is located within a circular play area. Alex and Dominic are sitting on opposite endpoints of a chord that contains the truck. Alex is 4 feet from the truck, and Dominic is 3 feet from the truck. Meira and Tamara are sitting on opposite endpoints of another chord containing the truck. Meira is 8 feet from the truck. How many feet, to the nearest tenth of a foot, is Tamara from the truck? Draw a diagram to support your answer.One Solution STEP 1. Draw a diagram.  EMBED Visio.Drawing.6 STEP 2. Use the Length of Inscribed Chords Theorem to solve.  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All 2s reservedo.`0_Sba.chm!#22426+l>(>Ud#1E (!(Z$ B$bW :?R0BTT I?H<( H<( UlE@ R0B|T  /T6DUmA@ ?ۿI?Y{O1@3EEbOeZ! H* V?"( pKquytpq<Lj p•lspgaxEndpoints determine cen & circumference ofle. "Length" is radius.Works great with stamp tool!U!Q.dHDD # =h0>TdHYY9 PAUAn@?P6 u `u bu * -2mu` ?N)u Y"8(+KBA  Dɝ>@$='8"G/Y%'Q-/ ) i?$%?> OU"bUNWiW0V9~Y`df&7Bx46 LK){ #AD5 `7Copyright 1999 Visio Corporation. All =Bs reserved.`H@_Sba.chm!#22425l>(>U@dE 2(W*Mx2;3Nk "(0IQ20;3_s7%3QQ5Os[rA RS[qArAaI=7!)/&00 B:4bH1mbؿ?t@ 贁N?8i6?Hl'-l !OyaGE(WszFݡ#KB4{+~akoU@ko+\0a(tNSԽ+B?92RDO0Si"?/j UPxP4FDTe]@y  ahZ- ^TUA(\W?? 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