10-1 Circles and Circumferences

Transcription

1 Geometry: 10-1 Circles and Circumferences Read pages and answer the following questions. 1. Define a circle: 2. Define radius: 3. Define Chord: 4. Define diameter 5. Answer the following questions using the figure to the right. a. Name the circle b. Name 3 radii c. Name the diameter d. Name a chord that is not a diameter 6. What is the relationship between the diameter and the radius? 7. What are congruent circles? 8. What are concentric circles? 9. What are the two ways that circle can intersect? Draw pictures 10. What does it look like when the two circles do not intersect? Draw pictures 11. Define circumference 12. What are the formulas for circumference? 1

2 10-1 continued Find the exact circumference of each circle. Leave in radical form with the pi symbol!!! No decimals

3 Geometry: 10-2 Measuring Angles and Arcs Read pg Define the following and draw a picture of each Central angle: Arc: Minor Arc: Major Arc: Semicircle: Complete the sketch to find the relationship between a central and its arc angle. 1. Draw a circle 2. Draw 2 radii 3. Measure the central angle 4. Measure the arc angle by clicking on the circle and the 2 points when the radii intersect the circle, go to measure arc angle. 5. Look at the angle and the arc angle that it creates. Take the select tool and move a point around 6. What is the relationship between the central and the arc angle that it creates? Relationship between a central angle and its arc angle: 3

4 10-2 continued Congruent arcs: If you have two congruent arcs then their central angles will be equal. 4

5 10-2 continued Use circle O to find the length of each arc. Round to the nearest hundredth

6 Geometry: 10-3 Arcs and Chords Complete the following sketches Equal chords and the arc angle that they create 1. Go to display, preferences and change your angles and the distances to hundredths. 2. Draw a circle 3. Draw 2 chords that are not parallel to each other 4. Measure the chords. Adjust them to that they are equal. 5. Measure the arc angles that they create by selecting the circle and the points where the chords intercept the circle. Go to measure arc angle. 6. What do you notice about the arc angles? 7. Why do you think this the mathematically true? Distances that equal chords are from the center. 1. Use the sketch you started above. 2. Draw a perpendicular line from the center to the chord by clicking on the center and the chord, go to construct perpendicular. 3. Measure the distance from the center to the intersection of the perpendicular line and the chord by clicking on the center and the intersection point, go to measure, distance 4. What do you notice about the distances? 5. Now measure the 2 parts of the chord that are created by the perpendicular line. 6. What do you notice? 6

7 Complete the following 10-3 continued 7

8 10-3 continued 8

9 Geometry: 10-4 Inscribed Angles Read page 709 and complete the following Define an inscribed angle: Draw the pictures of the 3 ways an angle can be inscribed in a circle. Sketchpad: Inscribed angles relationship to its arc angle 1. Draw a circle and an inscribed angle. 2. Measure the angle. 3. Measure the arc angle it creates by clicking on the circle and the two intercept points, measure, arc angle. 4. Look at the angle and its arc angle. What do you notice? Move one of the intercept points around. Still true? Sketchpad: Inscribed Quadrilateral (Quadrilateral inside a circle with the vertices on the circle) Draw an inscribed quadrilateral. Measure all the angles. What is the relationship of the angles across from each other? 9

10 Find the value of x continued 10

11 10-4 continued Complete the following 11

12 Geometry: 10-5 Tangents Read pages and complete the following Define tangent and draw a picture of a tangent line. Identify the point of tangency in the picture you have drawn. Define Common Tangent and draw a picture of the two common tangents: Define Circumscribed Polygons and draw a picture of one. Important Points about Tangent Lines A line is tangent to a circle if and only if it is perpendicular to a radius at a point of tangency. If two segments from the same exterior point are tangent to a circle, then they are congruent. Find x. Assume that segments that appear to be tangent are tangent. 12

13 10-5 continued 13

14 Geometry: 10-6 Secants, tangents and angle measures Secant: line that intersects a circle in exactly two points Draw a Secant: Angles inside the circle Angles Outside the Circle Find each measure. Assume that segments that appear to be tangent are tangent

15 10-6 continued Find y y

16 Geometry: 10-7 Special Segment in a circle Intersecting Chords- Segments Intersecting Inside the Circle Segments Intersecting Outside the Circle

17 10-7 continued

18 Geometry: 10-8 Equation of Circle Define Circle: 18

19 19