Circles Explorations
The following slides will help preview the circle concepts that we will look at next week. Answer the questions on each slide to the best of your ability.
Table of Contents
- Circle Terminology
- Circle Terminology
- Inscribed Angles
- Where to Sit? (I)
- Where to Sit (II)?
- Inscribed Angle Theorem (V1)
- Circumcenters
- Perpendicular Bisector: Quick Recap
- Making Perpendicular Bisectors: Ex. 9
- Where in NYC? (VA)
Circle Terminology
[color=#000000]There are many vocabulary terms we use when talking about a circle. [br]The following app was designed to help you clearly see and interact with each term. [br][br]Explore this app for a few minutes. Then answer the questions that follow. [/color]
Note: LARGE POINTS are moveable.
How would you describe or define a [b]CIRCLE[/b] as a locus (set of points that meets specified criteria)?
How would you describe the term [b][color=#38761d]RADIUS[/color] [/b][i]without using the words "half" or "diameter" [/i]in your description?
What does the term [b][color=#9900ff]CHORD[/color] [/b]mean here in the context of a circle?
How would you describe the term [b][color=#ff7700]DIAMETER[/color] [/b][i]without using the words "two", "double", or "diameter" [/i]in your description?
How would you describe/define the term [b][color=#cc0000]SECANT[/color][/b]?
What does it mean for a line to be [b][color=#1e84cc]TANGENT [/color][/b]to a circle?
Where to Sit? (I)
[color=#000000]Suppose you choose to sit in a [/color][color=#ff00ff][b]seat (pink point) [/b][/color][color=#000000]anywhere on the circle below, but [b]not behind[/b] [/color][color=#1e84cc][b]the stage[/b][/color][color=#000000]. [br][br]Which [/color][color=#ff00ff][b]pink point[/b][/color][color=#000000] provides the best viewing angle of [/color][b][color=#1e84cc]the stage[/color][/b][color=#000000]? [br]Mentally answer this question first. Then slide the slider completely. [br][br]What do you notice? [br][br]Feel free to change the size of [/color][color=#1e84cc][b]the stage[/b][/color][color=#000000] at any time by dragging its white endpoints along the circle. [br]Feel free to change the locations of the [/color][color=#ff00ff][b]pink points[/b][/color][color=#000000] at any time as well! [br][br]After interacting with this applet for a few minutes, complete the activity found at [url=https://tube.geogebra.org/m/QHQGxtAH]this link[/url]. [/color]
Perpendicular Bisector: Quick Recap
In the app below, the [b][color=#9900ff]purple line (p)[/color][/b] is said to be the [b][color=#9900ff]perpendicular bisector[/color][/b] of the segment with endpoints [b][color=#ff0000]SS[/color][/b] and [b][color=#0000ff]SHS[/color][/b]. Move points [b][color=#ff0000]SS[/color] [/b]snd [b][color=#0000ff]SHS[/color] [/b]around. (Don't touch the vertical slider yet.) [br][br]How would you describe what a [b][color=#9900ff]perpendicular bisector[/color][/b] of a segment [i]is[/i]? Please describe below.
After you answer the question above, go on to the questions below this app.
Complete the following in the app above.
[list=1][*]Slide up the black slider (on the right). [/*][*][b][color=#ff0000]Drag the red point (SS) on top of Stop & Shop. [/color][/b][/*][*][color=#0000ff][b]Drag the blue point (SHS) on top of Southington High School. [/b][/color][/*][*]Click the Show More checkbox (in the upper right corner). [/*][*]Drag that [b][color=#9900ff]LARGE PURPLE POINT[/color][/b] around. [/*][/list][br][b][color=#9900ff]What do you notice? [/color][/b]
Suppose a segment has endpoints [i][b]A[/b][/i] and [i][b]B[/b][/i]. [br]Suppose [b][color=#9900ff]point [i]W[/i] [/color][/b]is a point on the perpendicular bisector of this segment. [br][br]Which of the following statements are true?