Math Geometry Chapter 10

Geometry CP Chapter 10 Test Review Name: Key Use the following diagram to give a name for the following: [Image of a circle with points A, B, C, D, E, F, G, and H] 1. Tangent CH, EH 2. Point of tangency C, E, D 3. Chord FE, DG 4. Diameter DG 5. Radius AC, AE, BD, BG 6. Secant FE 7. Center A, B PS and QT are diameters of circle U. Find the indicated measure. 8. m∠QUR = 120.9° 180 - 43.6 - 15.5 = 120.9 9. m∠POR = 136.4° 120.9 + 15.5 = 136.4 10. m∠RST = 59.1° 43.6 + 15.5 = 59.1 11. m∠STP = 164.5° 180 - 15.5 = 164.5 12. m∠TPQ = 164.5° 180 - 15.5 = 164.5 13. m∠RQT = 300.9° 360 - 43.6 - 15.5 = 300.9 Find the measure of the given arc. 14. mDE = 80.5° 360 - 199 = 161 161/2 = 80.5 15. mWY = 265.4° 360 + 47.3 - 47.3 = 360 16. mAB = 106° (1/2)(106) = 53 angle + 53 = 160 angle = 106 17. mST = 94.7° 360 - 39 - 102 - 135 = 84 84/2 = 42 42 + 51 = 93 18. m∠JLM = 46° angle = (1/2)(92) = 46 19. m∠K = 28° 56/2 = 28 Find the value of the variables, angles, or arcs. 20. [Image of a circle with angles and arcs] angle = (1/2)arc x = (1/2)(148.6) x = 74.3 21. [Image of a circle with angles and arcs] 102 + 13y + 15x + 9 + 111 = 180 13y + 15x = -138 y = -6, x = -4 22. [Image of a circle with angles and arcs] m∠1 = (1/2)(128) m∠1 = 64 m∠2 = 180 - 64 m∠2 = 116 23. [Image of a circle with angles and arcs] angle = (1/2)(arc + arc) x = (1/2)(98 + 115) x = 106.5 24. [Image of a circle with angles and arcs] 6x² - 5x - 14 = 0 (6x + 7)(x - 2) = 0 both work! 25. [Image of a circle with angles and arcs] angle = (1/2)arc 51 = (1/2)FH 102 = FH 26. [Image of a circle with angles and arcs] 360 - 248 - 112 = 100 100/2 = 50 27. [Image of a circle with angles and arcs] 101 + x = 180 x = 79 28. [Image of a circle with angles and arcs] 8x² - 2x - 3 = 0 (2x + 1)(4x - 3) = 0 both work! 29. [Image of a circle with angles and arcs] 8x² - 2x - 3 = 0 (2x + 1)(4x - 3) = 0 both work! 30. Write the standard equation of the circle. [Image of a circle with center (2,2) and radius 4] C: (2,2) r: 4 (x-2)²+(y-2)²=16 Use the given information to write the standard equation of a circle. 31. Center (4.1, 2.5), radius: 3 (x-4.1)²+(y-2.5)²=9 32. Center (1,3), pt on the circle (-4, 15) (x-1)²+(y-3)²=r² (-4-1)²+(15-3)²=r² 25+144=r² 169=r² (x-1)²+(y-3)²=169 33. Write the standard equation of a circle whose diameter has endpoints (-8,-2) and (4,10). Center: ((-8+4)/2, (-2+10)/2) = (-2,4) r = √((-2+8)²+(4-10)²) = √(36+36) = √72 (x+2)²+(y-4)²=72 Graph the circle on the axes below. State the center and radius. a) (x-2)²+(y+1)²=9 [Image of a circle with center (2,-1) and radius 3] C: (2,-1) r: 3 b) x²+(y-4)²=32 [Image of a circle with center (0,4) and radius √32 ≈ 5.7] C: (0,4) r: √32 ≈ 5.7 Re-write the following equations of a circle in standard form by completing the square. 35. x²+y²-10x+8y+16=0 x²-10x+y²+8y=-16 x²-10x+25+y²+8y+16=-16+25+16 (x-5)²+(y+4)²=25 36. x²+14x+y²+2y=-40 x²+14x+49+y²+2y+1=-40+49+1 (x+7)²+(y+1)²=10