Geometry
Activity:
Segments In Circles
Posted on May 5, 2008
Topic: Circles
In this activity, students will explore the relationships among segments created by two intersecting chords, and secant segments. Students will store variables and use both the automated and manual data capture features in a spreadsheet and write formulas in spreadsheets to confirm relationships among segments.
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Activity Key Steps:
In problem 1, students explore chords and tangents. They use the Circle tool from the Shapes menu to draw a circle.
Then they draw two tangents to the circle and extend the lines until they intersect.
Students find the length from the intersection point to the two points of tangency. Then they grab the circle and change its size.
Students will use manual data capture to record lengths of the line segments in the circle.
The values are recorded in a spreadsheet and they find the products of the measures of the segments of each chord, that is, w • x and y • z.
Allow students time to observe the data and form conclusions about the data.
In Problem 4, students explore the Tangent-Secant Product Theorem.
At the end of this activity, students will be able to prove three Power Theorems: Chord-Chord, Secant-Secant, and Tangent-Secant Product Theorems. They will discover, confirm, and explore the theorems that describe the relationships involving different segments in circles.