Unit 8 Circle Geometry Exploring Circle Geometry Properties. 1. Use the diagram below to answer the following questions:
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1 Unit 8 Circle Geometry Exploring Circle Geometry Properties Name: 1. Use the diagram below to answer the following questions: a. BAC is a/an angle. (central/inscribed) b. BAC is subtended by the red arc. Go to: dex.html and answer the following questions. 2. Select and then click to answer the following: a. DAC and DBC are subtended by the red arc. b. DAC = DBC =. c. ADB = ACB =. d. Drag DAC and DBC along arc DABC. Angles and change in size. e. Click and drag BCAalong arc CD. BCAand ADB are subtended by the red arc. f. Click and change the size of the circle. Do any of the angle values change?. g. Click and change the location of the circle. Do any of the angle values change?. h. Conclusion: Angles subtended by the same arc are.
2 3. Select Click and click. Drag ADB to the right until DAC = 55 as shown in the diagram below. a. DBC =. b. BCA =. c. ADB =. d. The angles subtended by arc AB are and. e. The angles subtended by arc DC are and. f. Conclusion: Angles subtended by the same arc are. 4. Select and click to answer the following: a. The inscribed angle is and it is subtended by the red arc. b. The central angle is. c. CAB = and COB =. d. Drag point C around the circle until CAB measures 110. COB =. e. Click and drag C to the right to make central COB = 40. The inscribed angle is now. f. Click and drag C to the left to make inscribed CAB = 100. The central angle is now. g. Click and change the size of the circle. Do any of the angle values change?. h. Click and change the location of the circle. Do any of the angle values change?.
3 Conclusion: The central angle measures the inscribed angle subtended by the same arc. (half / twice) 5. Select and click. Move point B to the left until the central angle COB = 40 as shown in the diagram below. a. The inscribed angle is. b. The inscribed angle and the central angle are subtended by the same arc.. c. COB = 40 and the inscribed angle =. d. Change the size of the circle. Do any of the angle values change?. e. Change the location of the circle. Do any of the angle values change?. Conclusion: The central angle measures the inscribed angle subtended by the same arc. (half / twice)
4 6. Select and click to answer the following: a. The red tangents to the circle are lines and. b. The tangent lengths (shown as d(ac) = and d(ad) = ) are. c. ACO = ADO =. d. Move pt. A around the outside of the circle. ACO = ADO =. e. Move pt. C and pt. D around the circumference of the circle. ACO = ADO =. f. Move pt. B around the circle. OB, OC and OD are in length. g. Change the size of the circle. Do the tangent lengths change? Do the sizes of ACO or ADO change? h. Change the location of the circle. Do the tangent lengths change? Do the sizes of ACO or ADO change? Conclusion: A tangent to a circle is perpendicular to the at the point of tangency. 7. Select and click to answer the following: a. CD is called a. b. The midpoint of CD is. (A/0/B) c. The radius shown is segment.
5 d. Move pt. B around the circle until it intersects the chord CD at 90. Note: You will see a red right angle symbol at point A. When the radius passes through the midpoint of the chord, the lengths of CA and DA (or CE and DE) are. e. Click and move midpoint A until the chord CD intersects OB at 90. The lengths of CA and DA (or CE and DE) are. f. Click and move C and D around the circle until the chord intersects line OB at 90. The lengths of CA and DA (or CE and DE) are. g. Using the diagram from part f above, change the size of the circle. The lengths of CA and DA (or CE and DE) are. h. Using the diagram from part f above, change the location of the circle. The lengths of CA and DA (or CE and DE) are. Conclusion: The perpendicular from the centre of a circle bisects the. 8. Select and obtain the diagram below to answer the following: a. OB is a of the circle. b. CD is a of the circle. c. OB intersects CD at an angle of. d. The perpendicular from the centre of a circle bisects the. e. If CD measures 10 cm then CA and DA measure cm.
6 9. Select and click. Drag CD around the circle until A is on centre O and CD measures 16 as shown below. a. The length of AC =. b. The length of radius OB =. c. If the chord passes through the centre of circle and is twice the length of the radius, then the chord CD must be the. (diameter/radius) 10. Each diagram below is an example of one of the circle properties. Match the Circle Property to the diagram it illustrates. Circle Properties: Chord: The perpendicular from the centre of a circle to a chord bisects the chord. Central Angle: The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc. Inscribed Angle: The inscribed angles subtended by the same arc are equal in measure. Tangent: A tangent to a circle is perpendicular to the radius at the point of tangency. Property: Property:
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