Concept Byte: Paper Folding With Circles

Use With Lesson 12-2

ACTIVITY

A chord is a segment with endpoints on a circle. In these activities, you will explore some of the properties of chords.

Activity 1

• Step 1 Use a compass. Draw a circle on tracing paper.
• Step 2 Use a straightedge. Draw two radii.
• Step 3 Set your compass to a distance shorter than the radii. Place its point at the center of the circle. Mark two congruent segments, one on each radius.
• Step 4 Fold a line perpendicular to each radius at the point marked on the radius.

1. How do you measure the distance between a point and a line?
2. Each perpendicular contains a chord. Compare the lengths of the chords.
3. Make a Conjecture What is the relationship among the lengths of the chords that are equidistant from the center of a circle?

Activity 2

• Step 1 Use a compass. Draw a circle on tracing paper.
• Step 2 Use a straightedge. Draw two chords that are not diameters.
• Step 3 Fold the perpendicular bisector for each chord.

4. Where do the perpendicular bisectors appear to intersect?
5. Draw a third chord and fold its perpendicular bisector. Where does it appear to intersect the other two?
6. Make a Conjecture What is true about the perpendicular bisector of a chord?

Exercises

7. Write a proof of your conjecture from Exercise 3 or give a counterexample.
8. What theorem provides a quick proof of your conjecture from Exercise 6?
9. Make a Conjecture Suppose two chords have different lengths. How do their distances from the center of the circle compare?
10. You are building a circular patio table. You have to drill a hole through the center of the tabletop for an umbrella. How can you find the center?

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