Introduction to Circles

Jenni McIntire and Teresa Davis

This lab is to become familar with the definitions of the terms associated with circles.

A circle is the set of all points in a plane a given
distance ( radius ) from a given piont ( center ) in the plane.

 

Click here for a demonstration of this definition.


Write a definition for each term by looking at the examples and non-examples of each.

1. Diameter-

 Diameters:

Not Diameters:

2. Chord-

Chords:

 Not Chords:

3. Secant-

 Secants:

 

 Not Secants:

4. Tangent-

 Tangents:

 Not Tangents:

5. Central Angle-

 Central Angles:

 

Not Central Angles:

6. Inscribed Angle-

 Inscribed Angles:

 

Not Inscribed Angles:

7. Concentric Circles-

 Concentric Circles:

Not Concentric Circles:

8. Congruent Circles-

 Congruent Circles:

Not Congruent Circles:

Exercises:
Using your definitions from above, Construct each of the following on one large circle in Geometer's Sketchpad. Be sure to label all parts of your circle. Click here to begin your picture.

If you move any of the above points, does each stay consistent with its definition?

An arc of a circle is two points on the circle and the part
of the circle between the two points.

If the endpoints of the arc are the endpoints of a diameter, then the arc is a semicircle. If the arc is smaller than a semicircle, then the arc is a minor arc. If the arc is larger than a semicircle, then the arc is a major arc.

is a semicircle (three points are needed to name a semicircle)

is a minor arc (only the two endpoints are needed to name a minor arc)

is a major arc (three points are needed with the endpoints being the 1st and last)

Sketch:

In Sketchpad, do the following construction of arcs.

Construct a circle.
Construct a diameter.
Construct two points on the circle, both on the same side of the diameter.
Select the three points of the semicircle (be sure to go in consecutive order) and in the construct menu make an arc through three points. Only half of the circle should be highlighted. This is your semicircle.
Do the same to construct minor arc and a major arc with the same enpoints (note that when constructing a minor arc you still need three points, but to name it you only use two).
You can measure the arc angle or arc length, we will only be using arc angle. Measure all three of your arcs.

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