EMAT 6700

Chord Properties: Exercises

by Doug Westmoreland

Solve for the variable and state the conjecture or definition you used to solve the problem.

1. x = ?

 

2. s = ?

3. k = ?

4. y = ?

5. AB = CD, PO = 8 cm, OQ = ?

6. (AB = 6 cm, OP = 4 cm, CD = 8 cm, OQ = 3 cm, BD = 6 cm) What is the perimeter of OPBDQ?

7. Find the center of the circle below by using your compass and straightedge.

(After using compass and straightedge, have someone to draw a circle on Geometer's Sketchpad and hide the center point. Try to use sketchpad and find the center of the circle.)

8. Construct a triangle. Using the sides of the triangle as chords, construct a circle passing through all three vertices. Try doing this with compass and straightedge and Geometer's Sketchpad.

9. Draw a circle on Sketchpad and two chords of unequal length. Which is closer to the center of the circle, the larger or the smaller chord? Why?

10. Using Sketchpad, draw two circles with different radii. In each circle, draw a chord of the same length. Draw the central angle determined by each chord. Which central angle is larger? Why?

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