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Perpendicular Lines to Chords of a Circle

Author:
powere
Topic:
Circle

Follow the directions below to interact with the applet and then answer the questions.

1. Use the distance tool to measure the length of chord BC and chord DE. What do you notice about the length of these chords?

2. Use the perpendicular tool to create a perpendicular line from the center of the circle to chord BC and then a new perpendicular line from the center of the circle to the chord DE.
3. Use the point intersection tool to create two new points: one point is the intersection of chord BC and the perpendicular line and the other point is the intersection of chord DE and the other perpendicular line.

4. Use the distance tool to measure the distance from chord BC to the center of the circle and also the distance from chord DE to the center of the circle. What do you notice about these lengths?

5. Use the distance tool to measure from the new point on chord BC to B and then to C. Also use the distance tool to measure from the new point on chord DE to D and then to E. What do you notice about these distances?

6. Make a conjecture based on the following: If two chords in a circle have the same length and there is a perpendicular line through each chord and the center of the circle, then ____________________________________.

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