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8 angles inscribed in the same arc 9 congruent chords

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8)Angles inscribed in the same arc9)Congruent chords have congruent_________.or intercepting congruent arcsare______________.x=______y=______x ={Cone Head}10)Two tangent segments from an external point to a circle are ____________.If AB = 17, x=______11)In a circle, parallel chords intercept congruent_________.x=_____y=_____Triple Theorems:if any 2 of the following are true, the third statement is also true.xy78110xx_____11)a)line through thecenterof a circle12)a) line contains thecenterof a circleb)lineperpendicularto a chordb) linetangentto the circlec)linebisectingthe chordc) lineperpendicularat point of tangencyy10070xAB
Conclusion:________________Conclusion:_____________OMABOAB
Page25Circles Worksheet #1ABCD1)ABCD2)3)4)5)6)x3080x50yxxxy3065110yxx21086x62x120x6560x4550xx15040x3050xy100xx2xy2080x60xy50x100x5050xyx20100x3030
Page26
Page27Circles Worksheet #2ABCD1)ABC2)3)4)5)6)80x90120x28070x80xx10070x10030xx130xy80yx3y70x30xx507080x220x110x70xx4yy20x100x2453yyx14080xx120306080x
Page28Other Angles1.If mAC = 85 and mDB = 73, then m1 = _____.2.If mAD = 136 and mCB = 96, then m1 = _____.3.If m1 = 54 and mAC = 78, then mDB = _____.4.If m1 = 48 and mDB = 42, then mAC = _____.In 57,EFandEGare tangents.5.If mFHG = 280, then mE =_____.6.If mFG = 96, then mE=_____.7.If mE = 90, then mFHG =______.In 810,IJis a tangent.8.If mJK = 120 and mJL = 40, then mI = _____.9.If mI = 45 and mJL = 55, then mJK = _____.10.If mI = 50 and mJK = 110, then mJL = _____.11.If mPT = 100 and mQS = 20, then mR = _____.12.If mPT = 130 and mQS = 40, then mR =____.13.If mR = 25 and mQS = 25, then mPT = _____.14.If mR = 40 and mPT = 130, then mQS = ______.15.If mST = 90, mQS = 60, and mQP = 80, then mR = _____.In 1619,DFis tangent to the circle at point E.16.If mAG = 100 and mBH = 20, then mC = ______.17.If mC = 25 and mBH = 25, then mAG =_____.18.If mEH = 95 and mGE = 25, then mD =______.19.If mD = 40 and mEH = 138, then mGE =______.ADBC1GEFHKLIJRQPTSABCDGEFH#16 - 19#11 - 15#8 - 10#5- 7#1- 4
Page31Special Segment NotesTheorem of 2 intersecting chords:When 2 chords intersect inside a circle, the product of the segments of onechord = the product of the segments of the other chord.Ex. 1ab=cdx=______Ex. 2Ex. 3X=_____x =_____Theorem of 2 secant segments:When 2 secant segments are drawn from an external point, the product of onewhole secant segment and its external segment = product of the other wholesecant segment and its external segment.Ex. 1.(whole secant)( external piece) = (whole secant)(external piece)X=________Theorem of a secant segment and a tangent segment:When a secant segment and a tangent segment are drawn toCircle from an external point, the product of the wholeSecant segment and its ext. piece = (tangent)2.(whole secant)(ext. piece) =(tangent)2Ex1.Ex. 2X=_____x=_______abcd43x63x84xx33453x43x103xx
Page32Special segment lengths in CirclesSolve for x.1.2.3.x = ________x = ________x = ________4)5)6)x = ________x = ________x = ________7)8)x = ________x = ________9)10)x = ________x = ________4276x293152xx3xx6x822.58310x84x87x + 3x44xx1227x2x - 13x3x + 4

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