Nc Math 3

CHAPTER 7Circles7.1 Lines and Segments that Intersect Circles .2517.2 Finding Arc Measures .2577.3 Using Chords .2637.4 Inscribed Angles and Polygons .2697.5 Angle Relationships in Circles .2757.6 Segment Relationships in Circles .2817.7 Circles in the Coordinate Plane .287249Copyright Big Ideas Learning, LLCAll rights reserved.

Name DateChapter7Maintaining Mathematical ProficiencyFind the product.1.( x 4)( x 9)2.(k 6)( k 7)3.(y 5)( y 13)4.(2r5.(4m 5)(2 3m)6.(7w 1)(6w 5) 3)(3r 1)Solve the equation by completing the square. Round your answer to the nearesthundredth, if necessary.7. x 2 6 x 109. z 2 16 z 7 011. x 2 2 x 5 0Copyright Big Ideas Learning, LLCAll rights reserved.8.p 2 14 p 510. z 2 5 z 2 012. c 2 c 1 0250

Name7.1DateLines and Segments That Intersect CirclesFor use with Exploration 7.1Essential Question What are the definitions of the lines and segmentsthat intersect a circle?EXPLORATION: Lines and Line Segments That Intersect CirclestaordtenngWork with a partner. The drawing at the rightshows five lines or segments that intersect acircle. Use the relationships shown to write adefinition for each type of line or segment. Thenuse the Internet or some other resource to verifyyour ngent:Radius:Diameter:251Copyright Big Ideas Learning, LLCAll rights reserved.

Name Date7.12Lines and Segments That Intersect Circles (continued)EXPLORATION: Using String to Draw a CircleWork with a partner. Use two pencils, a piece of string, and a piece of paper.a. Tie the two ends of the piece of string loosely around the two pencils.b. Anchor one pencil on the paper at the center of the circle. Use the other pencilto draw a circle around the anchor point while using slight pressure to keep thestring taut. Do not let the string wind around either pencil.c. Explain how the distance between the two pencil points as you draw the circleis related to two of the lines or line segments you defined in Exploration 1.Communicate Your Answer3. What are the definitions of the lines and segments that intersect a circle?4. Of the five types of lines and segments in Exploration 1, which one is a subset ofanother? Explain.5. Explain how to draw a circle with a diameter of 8 inches.Copyright Big Ideas Learning, LLCAll rights reserved.252

concentric circlesNameDatecommon tangentPractice7.1For use after Lesson 7.1In your own words, write the meaning of each vocabulary term.Notes:circlecenterCopyright Big Ideas Learning, LLCAll rights reserved.247radiusName Datechord7.1Notetaking with Vocabulary (continued)diameterCore ConceptsLines and Segments That Intersect CirclessecantA segment whose endpoints are the center and any point on a circle is aradius.chordcenterdiameterA chord is a segment whose endpoints are on a circle. A diameter is a chordtangentthat contains the center of the circle.A secant is a line that intersects a circle in two points.point of tangencyA tangent is a line in the plane of a circle that intersects the circle in exactlyJJJGone point, the point of tangency. The tangent ray AB and the tangentAB are also called tangents.segmentcirclestangentradiussecantpoint oftangencytangent BANotes:concentric circlesCoplanar Circles and Common TangentsIn a plane,two circles can intersect in two points, one point, or no points. Coplanarcommontangentcircles that intersect in one point are called tangent circles. Coplanar circles that have acommon center are called concentric circles.2 points ofNotes:intersection1 point of intersection(tangent circles)no points ofintersection253concentriccirclesCopyright Big Ideas Learning, LLCAll rights reserved.A line or segment that is tangent to two coplanar circles is called a common tangent. A

one point, the point of tangency. The tangent ray AB and the tangentpointofsecantA tangent is a line in the plane of a circle that intersects the circle in exactlyJJJGtangencysegment AB are also called tangents.one point, the point of tangency. The tangent ray AB and the tangentpoint Name tangentDateNotes:BAChapter 10Notes:Practice (continued)7.1⃖ ⃗9. CoplanarKG is a secant.Circles and Common Tangents20. Use the Converse of the Pythagorean Theorem.18292 oint,ornopoints.CoplanarCoreConcepts⃖ ⃗CoplanarCirclesandCommonTangents10. A tangent line is EG, and a point of tangency is F.324 that have81 circles that intersect in one point are called tangent circles. Coplanar circlesa 225Ina plane,circlescan concentricintersectin circles.two points,one point, or no points.324CoplanarandSegmentsThat IntersectCircles 306commoncenterare called11. LinesThereare4twocommontangents.circles that intersect in one point are called tangent circles. Coplanar circles that have a— is not a tanga right triangle. Therefore, ABAsegmentwhoseendpointsare the centerand any point on a circle is a ABC is ius1 point of intersectionno pointsof2 points ofsegment.centerradius.(tangent circles)1 point of intersectionwhose(tangentendpointsare on acircles)intersection2 points ofAchord is aintersectionsegmentthat contains the center of the circle.circle.intersectionno 21.UseoftheA diameterintersectionis pointsa chorddiameterConverse of the Pythagorean Theorem.402 482602concentric 1600 23043600A secant is a line that intersects a circle in two points.circles3600 3904concentricsecant— is not a tangA tangent is a line in the plane of a circle that intersects the circle in exactlycirclesis not a right triangle. Therefore, AB DABJJJGone point, the point of tangency. The tangent ray AB and the tangent segment. point of12. AThereno commonline areor segmentthat tangents.is tangent to two coplanar circles is called a common tangent.Atangencysegment AB are also called tangents.common internal tangent intersects the segment that joins the centers 22.of thetwocircles.Use the Converseof the BPythagoreanTheorem.tangentAA commonline or segmentis tangentcoplanaris calleda commontangent.AAexternalthattangentdoes tonottwointersectthecirclessegmentthat joinsthe centersofthe22220 two12 16commoninternal tangent intersects the segment that joins the centers of thecircles.Notes:twocircles.400144 256A common external tangent does not intersect the segment that joins the centersof thetwo circles.400 400Notes:Coplanar Circles and Common Tangents ABC is a right triangle, with the right angle at A.13. Notes:There are 2 common tangents.— is tangent to C at point A.In a plane, two circles can intersect in two points, one point, or no points.Therefore,Coplanar ABcircles that intersect in one point are called tangent circles. Coplanar circles that have a23.(r 16)2 242 r 2Worked-OutExamplescommon center are calledconcentric circles.Example#12 points ofr 2 32r 256 576 r 21 point of intersection(tangent circles)intersectionno points of 32rintersection 256 576Copy the diagram. Tell how many common tangents the circles have and draw them.32r 320Ideas Learning,LLC14.CopyrightThere is 1Bigcommontangent.All rights reserved.Copyright Big Ideas Learning, LLCAll rights reserved.r 10248248The radius of C is 10.24.concentriccircles(r 6)2 92 r 2r 2 12r 36 81 r 2A line or segment that is tangent to two coplanar circles is called acommon internal tangentA common external tangent15. The common tangent is an external tangent because it does nottwocircles.Exampleintersect the #2segment that joins the centers of the two circles.Tell whether AB is tangent to (C. Explain your reasoning.16. Notes:The common tangent is an internal tangent because it20. Usethe Converseof thePythagoreanTheorem.intersectsthe segmentthatjoins the centersof the two circles.17.218The92 tangent152commonis an internal tangent because itintersects thesegment32481 225 that joins the centers of the two circles.B915A18C306 tangent is an external tangent because it does not18. 324The common— ABC isthenotsegmenta right triangle.a tangentintersectthat joinsTherefore,the centersABof isthenottwocircles.segment.19. Use the Converse of the Pythagorean Theorem.21.CopyrightUseof the PythagoreanTheorem.IdeasLLC2 52 the Converse3Big42 Learning,All rightsreserved.22602536004016 9 1600 230448225426.(r 18)2 302 r 2r 2 36r 324 900 r 236r 324 900

Name7.1DatePractice (continued)PracticeAExtra PracticeIn Exercises 1–6, use the diagram.1. Name two radii.2. Name a chord.3. Name a diameter.4. Name a secant.5. Name a tangent.6. Name a point of tangency.EADFBCIn Exercises 7 and 8, use the diagram.7. Tell how many common tangents the circles have and draw them.8. Tell whether each common tangent identified in Exercise 7 isinternal or external.In Exercises 9 and 10, point D is a point of tangency.9. Find BD.CA10. Point C is also a point of tangency. If BC 4 x 6, findthe value of x to the nearest tenth.105.5D255BCopyright Big Ideas Learning, LLCAll rights reserved.

NameDatePractice10.1 BPractice BIn Exercises 1–5, use the diagram.BA1. Name two radii.2. Name two chords.CHDE3. Name a diameter.G F4. Name a secant.5. Name a tangent and a point of tangency.In Exercises 6 and 7, tell whether AB is tangent to : C. Explain your reasoning.6.30A7.B 16 C2821B3420CAIn Exercises 8 and 9, point B is a point of tangency. Find the radius r of : C.8.9.Cr3.625rA35Brr4.8ACBIn Exercises 10 and 11, points B and D are points of tangency. Find the value(s) of x.B10.11.4x 74x2 18x 10AC6x 3DBACx2 x 4D12. When will two circles have no common tangents? Justify your answer.13. During a basketball game, you want to pass the ballYouto either Player A or Player B. You estimate thatPlayer B is about 15 feet from you, as shown.15 ftPlayer AAa. How far away from you is Player A?Player B12 ft Bb. How can you prove that Player A and Player Bare the same distance from the basket?DE Basket CCopyright Big Ideas Learning, LLCAll rights reserved.256

circles that intersect in one point are called tangent circles. Coplanar circles that have a common center are called concentric circles. A line or segment that is tangent to two coplanar circles is called a common internal tangent A common external tangent two circles. Notes: intersects the segment that joins the centers of the two circles .