If your post has been solved, please type Solved! or manually set your post flair to solved. Title: Need answers for Unit circles Homework 4: congruent chords and arcs Full text: Please, Look it up on google and you will find it. Did 1-2 To help preserve questions and answers, this is an automated copy of the original text. I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns. Unit 10 HomeworkSelected AnswersHW #28–Lines & Segments that Intersect Circles1) They both intersect a circle at two points, but chords are segments only and secants could be represented aslines and have some external portion.5) CircleC6),CA CD7),BHAD8)AD9)KG10),EFG F11) 412) 013) 215) external16) internal17) external19) yes20) no23)10r=24)3.75r=29)5x=31)3x= 33) In the diagram, the right angle has vertex atZ.XYis not a tangent because if it were, it would beperpendicular toZX, which it is not.37) perimeter = 25.638) b)CADBis a square Problem 1 : Find x. Problem 2 : Find x. Problem 3 : Find x. Problem 4 : If MP = 5x - 34, PN = 2x - 4, find MP. Problem 5 : If QM = 6x - 11 and MR = 2x + 9, find MN. Problem 6 : In circle Z, if RS = 18, and m∠arcTY = 42°, find the following measures. (i) TU, (ii) TU, (iii) WS, (iv) m∠arc YU, (v) m∠arc RS Problem 7 : Use the circle below to find : (i) VW and (ii) m∠arc YW Problem 8 : In the circle below HK = 30 and PM = 8. Find the following measures : (i) PH and (ii) m∠arc GJ Answers1. Answer : In the diagram above, the two chords ST and RS are congruent. Then, ST = RS 7x + 24 = 115 Subtract 24 from each side. 7x = 91 Divide each side by 7. x = 13 2. Answer : In the diagram above, the two chords VW and XY are congruent. Then, WV = XY 9x - 34 = 4x + 1 Subtract 4x from each side. 5x - 34 = 1 Add 34 to each side. 5x = 35 Divide each side by 5. x = 7 3. Answer : In the diagram
above, m∠arc YZ = (6x - 20)° And also, the two chords YZ and XY are congruent. Then, m∠arc XY = m∠arc YZ m∠arc XY = (6x - 20)° In the circle above, m∠arc XY + m∠arc YZ + m∠arc ZX = 360° (6x - 20)° + (6x - 20)° + 76° = 360° 6x - 20 + 6x - 20 + 76 = 360 Combine the like terms. 12x + 36 = 360 Subtract 36 from each side. 12x = 324 Divide each side by 12. x = 27 4. Answer : In the diagram above, m∠arc JK = m∠arc KL Then, the two chords JK and KL are congruent. Because the two chords JK and KL are congruent, they are equidistant from the center. Then, MP = PN 5x - 34 = 2x - 4 Subtract 2x from each side. 3x - 34 = -4 Add 34 to each side. 3x = 30 Divide each side by 3. x = 10 Find MP : MP = 5x - 34 Substitute x = 10. MP = 5(10) - 34 MP = 50 - 34 MP = 16 5. Answer : In the diagram above, the two chords LM and MN are equidistant from the center. Then, the two chords LM and MN are congruent. The radii JP and KP are perpendicular to the chords LM and MN respectively. Then, they bisect the chords. Because the chords LM and MN are congruent and they are bisected by the radii, QM = MR 6x - 11 = 2x + 9 Subtract 2x from each side. 4x - 11 = 9 Add 11 to each side. 4x = 20 Divide each side by 4. x = 5 Find MN : MN = 2(MR) MN = 2(2x + 9) MN = 4x + 18 Substitute x = 5. MN = 4(5) + 18 MN = 20 + 18 MN = 38 6. Answer : (i) TU : Because the two chords RS and TU are equidistant from the center, they are congruent. TU = RS TU = 18 (ii) TV : Because the
radius YZ is perpendicular to the chord TU, the radius YZ bisects the chord TU. Then, TV = TU/2 TV = 18/2 TV = 9 (iii) WS : Because the radius XZ is perpendicular to the chord RS, the radius XZ bisects the chord RS. Then, WS = RS/2 WS = 18/2 WS = 9 (iv) m∠arc YU : m∠arc YU = m∠arc TY m∠arc YU = 42° (iv) m∠arc RS : m∠arc TU = m∠arc TY + m∠arc YU m∠arc TU = 42° + 42° m∠arc TU = 84° Because the two chords RS and TU are equidistant from the center, they are congruent. Then, m∠arc RS = m∠arc TU m∠arc RS = 84° 7. Answer : (i) VW : Using the Pythagorean theorem in right triangle WXZ, WZ2 + XZ2 = WX2 WZ2 + 52 = 132 WZ2 + 25 = 169 Subtract 25 from each side. WZ2 = 144 WZ2 = 122 WZ = 12 Because the radius XY is perpendicular to the chord VW, the radius XY bisects the chord VW. Then, VW = 2(WZ) VW = 2(12) VW = 2 (ii) m∠arc YW : In right triangle WXZ, cos X = 5/13 m∠ X = cos-1(5/13) m∠ X = 67.4° Then, m∠arc YW = 67.4° 8. Answer : (i) PH : In the circle above, PN = PM PN = 8 Because the radius PJ is perpendicular to the chord HK, the radius PJ bisects the chord HK. Then, HN = HK/2 HN = 30/2 HN = 15 Using the Pythagorean theorem in right triangle HNP, HN2 + PN2 = PH2 152 + 82 = PH2 225 + 64 = PH2 289 = PH2 172 = PH2 17 = PH (ii) m∠arc GJ : In right triangle HNP, tan P = 15/8 m∠ P = tan-1(15/8) m∠ X = 61.9° Then, m∠arc GJ = 2 ⋅ m∠ X m∠arc GJ = 2 ⋅ 61.9° m∠arc GJ =
123.8° Kindly mail your feedback to We always appreciate your feedback. ©All rights reserved. onlinemath4all.com |