Segment Lengths in Circles
Objectives: Students are to discover three theorems
concerning how to find the lengths of segments in circles.
Lesson:
Have students discover the following theorems:
Theorem 1: If two chords
intersect in the interior of a circle, then the product of the lengths
of the segments of one chord is equal to the product of the lengths of
the segments of the other chord. 

Theorem 2: If two secant
segments share the same endpoint outside a circle, then the product of
the length of one secant segment and the length of its external segment
equals the product of the length of the other secant segment and the
length of its external segment. 

Theorem 3: If a secant
segment and a tangent segment share an endpoint outside a circle, then
the product of the length of the secant segment and the length of its
external segment equals the square of the length of the tangent segment. 
Here are the interactive GSP sketches for the above
theorems: Theorem 1, Theorem 2, Theorem
3.
Conclusion: Have the students discuss the conclusions they
formed based on the activity. Review the theorems that the
students should have discovered during the activity.
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