B C TANGENT TANGENT/RADIUS THEOREMS
#19TANGENTS, SECANTS, AND CHORDSThe figure at right shows a circle with three lines lying ona flat surface. Line a does not intersect the circle at all.Line b intersects the circle in two points and is called aSECANT. Line c intersects the circle in only one pointand is called a TANGENT to the circle.abcTANGENT/RADIUS THEOREMS:1. Any tangent of a circle is perpendicular to a radius of thecircle at their point of intersection.2. Any pair of tangents drawn at the endpoints of a diameterare parallel to each other.chordA CHORD of a circle is a line segment with its endpoints on the circle.DIAMETER/CHORD THEOREMS:1. If a diameter bisects a chord, then it is perpendicular to the chord.2. If a diameter is perpendicular to a chord, then it bisects the chord.ANGLE-CHORD-SECANT THEOREMS:! mBC!)m 1 1 (mAD2PQAAE EC DE EB2! ! mQS!)m P 12 (mRTEBS1CRDPQ · PR PS · PTTExample 1Example 2If the radius of the circle is 5 units andAC 13 units, find AD and AB.InB, EC 8 and AB 5. Find BF.Show all subproblems.EADDFCBBAD ! CD and AB! CD by Tangent/RadiusTheorem, so ( AD ) ( CD ) ( AC ) or2( AD )2CA22 ( 5 ) (13) . So AD 12 and22AB ! AD so AB 12.GEOMETRY Connections 2007 CPM Educational Program. All rights reserved.The diameter is perpendicular to the chord,therefore it bisects the chord, so EF 4. ABis a radius and AB 5. EB is a radius, soEB 5. Use the Pythagorean Theorem tofind BF: BF2 42 52 , BF 3.53
In each circle, C is the center and AB is tangent to the circle at point B. Find the area ofeach circle.1.AAC 302.3.B45 CB30 6 336!BAB 12AC 455.18CC25C4. A6.AC 16B7.AAC 86AA8.28 BB122456CCACDAD 18CAC 90BAC9. In the figure at right, point E is the center andm CED 55 . What is the area of the circle?5EAD5BEIn the following problems, B is the center of the circle.Find the length of BF given the lengths below.DFB10.EC 14, AB 1611. EC 35, AB 2112.FD 5, EF 1013. EF 9, FD 614.InR, if15.AB 2x ! 7 andCD 5x ! 22 ,find x.B16.InO, MN ! PQ ,MN 7x 13 , andPQ 10x ! 8 . Find PS.NAInD, if AD 5and TB 2, find AT.A5DxRAPCTxCMOT2 BSD54 2007 CPM Educational Program. All rights reserved.QExtra Practice
17.InJ, radius JL and chord MNhave lengths of 10 cm. Find thedistance from J to MN .18.In O, OC 13 and OT 5.Find AB.C AL13O 5 T10J10NBMA19.GIf AC is tangent to circle E and EH ! GI , is GEH AEB? Prove your answer.BHE20. If EH bisects GI and AC is tangent to circle E atpoint B, are AC and GI parallel? Prove youranswer.ICDFind the value of x.21. x 22.23.25 24.43 Px 15 x 80148 4020 x 41 ! 84 , mBC! 38 , mCD! 64 , mDE! 60 . Find the measure of eachInF, mABangle and arc.BA!!4125. mEA26. mAEB27. m!128. m!229. m!330. m!4GEOMETRY Connections 2007 CPM Educational Program. All rights reserved.FE23CD55
For each circle, tangent segments are shown. Use the measurements given find the value of x.31.141 32.AE61 F33.QPDGx B70 x RC34.S110 35.x x 160 35 T58 HI36.x 50 (4x 5) x 38 Find each value of x. Tangent segments are shown in problems 40, 43, 46, and .44.0.81.045.5xxx6x102x546.47.453xx548.63x56 2007 CPM Educational Program. All rights reserved.1210Extra Practice
Answers1. 275π sq. un.2. 1881π sq. un.3. 36π sq. un.4. 324π sq. un.5. 112π sq. un.6. 4260π sq. un.7. 7316π sq. un.8. 49π sq. un.9. 117.047 sq. un.10. 14.411. 11.612. 7.513. 3.7514. 515. 3116. 417. 5 3 cm.18. 5 319. Yes, GEH AEB (reflexive). EB is perpendicular to AC since it is tangentso GHE ABE because all right angles are congruent. So the triangles aresimilar by AA .20. Yes. Since EH bisects GI it is also perpendicular to it (SSS). Since AC is atangent, ABE is a right angle. So the lines are parallel since the correspondingangles are right angles and all right angles are equal.21. 16022. 923. 4224. 7025. 11426. 27627. 8728. 4929. 13130. 3831. 4032. 5533. 6434. 3835. 4536. 22.537. 1238. 5 1239. 240. 3041. 242. 2 243. 1.244. 545.46. 647. 7.548. 5GEOMETRY Connections 2007 CPM Educational Program. All rights reserved.3057
SECANT. Line c intersects the circle in only one point and is called a TANGENT to the circle. a b c TANGENT/RADIUS THEOREMS: 1. Any tangent of a circle is perpendicular to a radius of the circle at their point of intersection. 2. Any pair of tangents drawn a
Generally the most basic difference is the radius of curvature. Elbows generally have radius of curvature between one to twice the diameter of the pipe. Bends have a radius of curvature more than twice the diameter. Short Radius and Long Radius Elbows are again classified as long radius or short radius elbows.
duct mounted vertical fire / smoke damper flexible round duct mitered rectangular duct elbow with turning vanes 1.0 radius and 1.5 radius smooth round or oval elbow 1.0 radius and 1.5 radius 3-gore round or oval elbow 1.0 radius and 1.5 radius 5-gore round or oval elbow sharp-throat radius-heel rectangular duct elbow straight take-off conical .
A spiral curve can be used to provide a gradual transition between tangent sections and circular curves. While a circular curve has a radius that is constant, a spiral curve has a radius that varies along its length. The radius decreases from infinity at the tangent to the radius of th
1 SECTION 2.1 - THE TANGENT AND VELOCITY PROBLEMS Tangent Problem Definition (Secant Line & Tangent Line) Example 1 Find the equation of the tangent lines to the curve 1 3x 2 y at the
A Patient’s Guide to Distal Radius Fractures (Broken Wrist) Introduction The forearm is composed of two bones, the radius and the ulna. The radius is larger at the wrist. Patients who fall often fracture the radius. The radius is the third most . A distal wrist plate
A net positive suction head available, m (NPSH) R net positive suction head required, m P pressure, Pa P v vapor pressure, Pa r radius (variable) or radius of curvature, m R radius, m Rc universal gas constant, 1.987 cal / (g-mole K) R b bob radius, m R c cup radius, m R s shaft radius, m R o
Theorem 12-1 relates a tangent and a radius in a given circle.You will write an indirect proof for Theorem 12-1 in Exercise 29. You can use Theorem 12-1 to solve problems involving tangents to circles. 12-1 11 Using the Radius-Tangent Relationship p2 6p 9 w 2 20w 100 m –4m 4 2"30
AKKINENI NAGESWARA RAO COLLEGE, GUDIVADA-521301, AQAR FOR 2015-16 1 The Annual Quality Assurance Report (AQAR) of the IQAC Part – A AQAR for the year 1. Details of the Institution 1.1 Name of the Institution 1.2 Address Line 1 Address Line 2 City/Town State Pin Code Institution e-mail address 08674Contact Nos. Name of the Head of the Institution: Dr. S. Sankar Tel. No. with STD Code: Mobile .
