NJCTL



CirclesParts of a Circle378796832246ClassworkUse the diagram of the circle with center A to answer the following:Name the radiiName the chord(s)Name the diameter(s)If AC = 7, what does TC = ?If CT = 13, what does MA = ?Which is longer TC or MA? Justify.Explain the difference between the radius of a circle and a chord.Parts of a CircleHomework4249144132494Use the diagram of the circle with center C to answer the following: Name the radiiName the chord(s)Name the diameter(s)If CE = 8, what does BD = ?If BD = 19, what does CE = ?Which is longer DB or AB? Justify.Explain the difference between the diameter of a circle and a chord.Angles & ArcsClasswork411480039370In C, AD is the diameter, m∠BCD=110° & m∠ACE=80°. Find the measurement of each arc and classify the arc as a minor arc, major arc, or semicircle.mAEmABmABDmEBDmBEDmAED450850014351000mADBTwo concentric circles have center P, PS = 6 and SU = 4.Which is greater: mRS or mTU?Which is greater: the length of RS or the length of TU?∠TPU=90°, how long would chord TU be?Angles & ArcsHomework431800021018500In C, AD is the diameter, m∠BCD=130° & m∠ACE=60°. Find the measurement of each arc and classify the arc as a minor arc, major arc, or semicircle.mAEmABmABDmEBDmBEDmAEDmADB45085006794500Two concentric circles have center P, PS = 3 and SU = 3.Which is greater: mRS or mTU?Which is greater: the length of RS or the length of TU?∠TPU=90°, how long would chord TU be?Arc Length & RadiansClassworkPARCC type Questions4343400-6985In C, AD is the diameter, m∠BCD=110°, m∠ACE=80°, and CE = 5, find the followinglength of AElength of mABlength of ADlength of EBDlength of BEDlength of ADElength of ADBIf the central angle of a circle has measure 60o and makes a minor arc with length 15, what is the radius?If the arc of a circle has length 8π and the circumference of the circle is 24π, what is the measure of the central angle that intercepts the arc?In #44-49, convert the degrees of the angle to radians, or the radians of the angle to degrees. Use 3.14 as your value of ? .20°135°343°5 radians3.5 radians3π2 radiansArc Length & RadiansHomeworkPARCC type Questions434340017145In C, AD is the diameter, m∠BCD=130°, m∠ACE=60°, and CE= 8, find the followinglength of AElength of mABlength of ADlength of EBDlength of BEDlength of ADElength of ADBIf the central angle of a circle has measure 80o and makes a minor arc with length 12, what is the radius?If the arc of a circle has length 10π and the circumference of the circle is 30π, what is the measure of the central angle that intercepts the arc?In #59-64, convert the degrees of the angle to radians, or the radians of the angle to degrees. Use 3.14 as your value of ? .17°150°321°4 radians2.5 radiansπ6 radiansChords, Inscribed Angles & Triangles2157951116840153670116840Class Work472440015367000Solve for the variable in each problem. C is the center of the circle.65.66.67. 26827371531181629041531184914265577850068.69.70. 2534920-2387604800600-22860071.72.73. 154222-366312486092531752682240317530529813089374.75.76. 49806641005027527251689103509110419577.78.79. 11430017399025146001479550080.81.4457700635000PARCC type Questions82. The figure to the right shows a circle with center H, diameter GF, and inscribed ?FGJ. HF = 12. Let m∠GJF=(x+25)° and m∠JGF=x°.Find the value of x.Choose the correct option for each blank. Answer choices are givenin the boxes below each blank.The length of JF is _______________ because __________________.?JHF is equilateralm∠JHF<60°m∠JHF>60°12less than 12greater than 1283. Point P is the center of a circle. RT is the diameter of the circle. Point U is a point on the circle, different from R and T.a) Determine if the following statements are always, sometimes, or never true.1) RT > RU2) m∠TRU= 12 (m∠UPT)3) m∠RTU=90°4) m∠TRU=2(m∠RTU)b) If m∠PUT=50°, what is m∠RPU?Chords, Inscribed Angles & TrianglesHomeworkSolve for the variable in each problem. C is the center of the circle.4312754-2941982252980-461645233735-10336784.85.86. 0-34290026822408763049085501587587.88.89. 473392531115260286511811032067515811590.91.92. 4735830-2844802301875-2844800-22860093.94.95. 4582795145415205549557785-3630915795096.97.98. 251460012954000-1143001524099.100.4229100-11430000PARCC type Questions101. The figure to the right shows a circle with center C, diameter BD, and inscribed ?BDE. BD = 28. Let m∠BED=(3x)° and m∠EBC=x°.Find the value of x.Choose the correct option for each blank. Answer choices are givenIn the boxes below each blank.The length of DE is ______________ because ______________.?ECD is equilateralm∠ECD<60°m∠ECD>60°14less than 14greater than 14102. Point M is the center of a circle. JK is the diameter of the circle. Point L is a point on the circle, different from J and K.a) Determine if the following statements are always, sometimes, or never true.1) ML > KL2) m∠KJL= 12 (m∠JKL)3) m∠KLJ=90°4) LM=2(KJ)b) If m∠JKL=25°, what is m∠JML?3771900-342900Tangents & SecantsClassworkDraw a tangent line to the circle at M.901702705104457700412752642870214630What is the difference between a chord and a secant?Draw the common tangents for each set of circles.105.106.107. If a circle has a center of (7,6) and is tangent to the x-axis, how big is the radius?If a circle has a center of (7,6) and is tangent to the y-axis, how big is the diameter?4800600-11430032067560960260322421914Solve for the variable in each problem. C is the center of the circle.110.111.112. 46024801320802491740154940284480154940113.114.115.4778375-3797302506980-228600198755-228600116.117.118.46228006540526771602349518542023495119.120.121.4800601270004725891478182602865127000122.123.124.44176955778524917405715027305076200125.126.127. PARCC type Question128. The figure shows two semicircles with centers K & M. The semicircles are tangent to each other at point J, and QN is tangent to both circles at N & O. If KL = JP = 12, what is OQ?297180013144500388620053975Tangents & SecantsHomeworkDraw a tangent line to the circle at A.What is the difference between a tangent and a secant?4781550-1143002364105114300114300-52070Draw the common tangents for each set of circles.131.132.133. If a circle has a center of (3, -6) and is tangent to the x-axis, how long is the radius?If a circle has a center of (3, -6) and is tangent to the y-axis, how long is the diameter?46228001143026028651143022578467200Solve for the variable in each problem. C is the center of the circle.136.137.138. 4686300-22860037685923964260322423964139.140.141.2628900-228600228600-342900469441778685142.143.144. 27222451654810434403515354305842013525500539754545330138430245173590170145.146.147. 148.149.150. 4387215-3092452400300-35750512700-483870151.152.153. PARCC type Question154. The figure shows two semicircles with centers R & S. The semicircles are tangent to each other at point P, and UW is tangent to both circles at V & W. If QR = PT = 18, what is WV?29718003302000Segments & Circles4996567112782Classwork267478675102730506985Find the value of the variable. C is the center of the circle.155.156.157.449563413740825628600480226331158.159.160. 4572000-457200185420317527622503175161.162.163. Segments & Circles48057351590262762249159025Homework27349113998Find the value of the variable. C is the center of the circle.164.165.166. 230060580645446382980811178077-607167.168.169. 4646930-254042354560960267716060960170.171.172. 360489530480Multiple ChoiceFor questions 1-4, use the diagram at the right of ⊙FName a secant of the circlea. FA b. AC c. BEd. BCBF = 7 and tangent BE = 9, what is AE?a. 5.656b. 11.402c. 4.402d.2.402m∠BCA=20° and BD = 8, what is the length of BC?a. 1.396b. 2.793c. 9.774d. 19.548m∠BCA=20°, what is the measurement of BA in radians?a. 0.35 radiansb. 0.70 radiansc. 1.40 radiansd. 2,292.99 radiansIf AB is a diameter and mAC=50°, then what is mABC?a. 50°b. 130° c. 230°d. 310°13716008636000Find the value of a.20030024020If an angle measures 3 radians, what is its measurement in degrees?30°85.94°171.89°343.77°12573009969500Find the value of b. 70110150182880011874500210Find the value of c.653530not enough information12573004127500Find the value of d.204050701600200-11430000Find the value of e.7.588.591371600685800 Find the value of f.23461714500889000Find the value of g.25.3810Find the value of x.1371600381000036.75915Point H is the center of a circle. EF is the diameter of the circle. Point G is a point on the circle, different from E and F.EF > HEAlwaysSometimesNeverm∠EFG=90°AlwaysSometimesNeverFG=EGAlwaysSometimesNeverm∠EHG=2(m∠EFG)AlwaysSometimesNeverIf m∠FEG=38°, what is m∠GHF?38°52°76°104°Extended Response381977211816S, T, U, and V are points of tangency of ⊙A and ⊙B. TH = 4x + 8, SH = 6x + 4, HU = x + 2y, and HV = 4x - 2y.Find the value of x. Find the value of y.If AB = 25 and UB (not drawn) = 5, what is the length of AT(not drawn)?In the diagram AB∥CD and CD is a diameter.467851438569If mAB=40° find the mBC.If AB = 12 and CD = 20, how far from the center is AB?Using the information from parts a) and b), how long is ACB?A triangle is inscribed in a circle creating three arcs. Two of the arcs are 80° and 130°. Draw a diagram for the given information above.Find the measurement of the missing arc.Find the measurements of all of the inscribed angles and list the angles in order from greatest to least.297180045275500The figure shows two semicircles with centers D & F. The semicircles are tangent to each other at point C, and BH is tangent to both circles at G & H. DC = CA = 20.Determine the lengths of the radii in eachcircle. Draw additional radii in the diagram.Determine the length of AB.Determine the length of GB.Answer KeySegments AT, AM, ACSegments JH, TCSegment TC146.5Segment TC is longer because the diameter is twice the radius.The radius is the segment that has one endpoint as the center of the circle and the other endpoint on the circle. A chord is a segment that has 2 endpoints on the circle.Segments CD, CB, and CESegments AB, DBSegment DB169.5Segment DB, diameter is longest chord of a circleThe diameter is the longest chord and the only chord that passes through the center.80°; minor70°; minor180°; semicircle260°; major250°; major180°; semicircle290°; majorThey are equalTU is longer10260°; minor50°; minor180°; semicircle240°; major230°; major180°; semicircle310°; majorThey are equalTU is longer626.986.1015.722.6921.8222.6925.3145/π120° 0.35 radians2.36 radians5.98 radians286.62°200.64°270°8.386.9825.1333.5132.1141.8943.288.59120°0.30 radians2.62 radians5.60 radians229.30°143.31°30°X=442 degrees30 degreesX=3X=850 degreesX=584 degreesX=14520 degrees140 degrees90 degreesX=170 degreesX=20 degreesX=95X = 80 degreesx = 12a) x = 55°b) greater than 12 m∠JHF>60°a) 1) Always 2) Always 3) Never 4) Sometimesb) m∠RPU=100°v=4b= 80 degreesn=220 degreesF=40 degreesR=9.85x=4x=850k=140d=80h=60 degreesg=5.66d=80e=35n=60f = 110x = 18.5a) x = 30 b) 14 ?ECD is equilaterala) 1) Sometimes 2) Sometimes 3) Always 4) Never b) m∠JML=50°Tangent line touches the circle at MA chord has endpoints on the circle, while a secant passes through.Four tangent lines. Two of the tangent lines touch the outsides of the two circles, while the other two make a diagonal in the middle of the two circles.Two tangent lines on the outsides of the two circles.One tangent line at the bottomR=6D=14x=12x=9x=4c=41g=8x=2, y=6c=10x=7x=8a=35k=40x=130h=220f=80g=6065b=130m=120OQ = 1152=242=33.94Tangent line passes through AA tangent “touches” at one point, while a secant touches at two pointsTwo tangent lines on the outside. Two more tangent lines making a diagonal through the middle.One tangent line through the center of the two touching circles. Two more tangent lines, one at the top and one at the bottom.No tangent linesR=6R=6f=9t=252.49g=7g=10x=3; y=2j=12r=11x=7d=80x=70/3x=22040 degrees140 degreesx=210a=30 degreesd=135d=60 degreesWU = 2592=362=50.91 VU = 648=182=25.46 WV = 362-182=182=25.46n=6.4x=8x=4x=2x=3x=5.48x=6x=9x=4n=4r=5h=2x=8y=1k=3.37v=4.47x=2.25a=1.66Unit ReviewMultiple ChoiceCCCBDACCCADCAAACBACExtended Response(a) 2 (b) 1.5 (c) 3(a) 110 (b) 8 (c) 55.851(a) Note: the letters used in the diagram below can be any random letters chosen. (b) mPO=150°(c) m∠OQP=75° m∠OPQ=65° m∠POQ=40°(a)2010=40+x10+x 21=40+x10+x 20+2x=40+x2x=20+xx=20=AB102+GB2=302100+GB2=900GB2=800GB=202=28.28 ................
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