Geometry
Activity:
Chords and Circles
Posted on Apr 17, 2008
Topic: Circles
Students will begin this activity by exploring how the chord in a circle is related to its perpendicular bisector. Investigation will include measuring lengths and distances from the center of the circle.
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Activity Key Steps:
In problem 1, students explore the relationship between a chord and its perpendicular bisector.
Students start by constructing the midpoint and a perpendicular bisector of a chord. They find the lengths of the two line segments as shown to the right and label them.
Students then determine how the lengths of AD and BC are related. They should see the lengths have an inverse relationship since the chord BC increases and the distance from the chord to the center AD decreases.
Students construct a point G outside the circle using a line perpendicular to the x-axis and one perpendicular to the y-axis. They drag point B around the circle and use the Locus tool to construct the path of B. Students will describe the graph.
In problem 2, students will investigate congruent chords. They construct a chord HJ of the circle. Students will then drag the points H or J around the circle and observe what happens as the lengths of the two chords approach the same measure.
They will see that the perpendicular distance from the center of a circle to congruent chords is always equal.
Problem 3 is an extension of this activity. They will find and graph the equation in terms of the radius.
At the end of this activity students will be able to apply the Perpendicular Bisector Theorem.