Segment Lengths – Theorems and Beginning Problems

Segments formed by Chords, Secants, and Tangents

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Students learn the following theorems related to chords, secants, and tangents. If two chords intersect inside 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. If two secant segments are drawn to a circle from an external point, then the product of the lengths of one full secant segment and its external tangent segment is equal to the product of the lengths of the other full secant segment and its external tangent segment. If a secant segment and a tangent segment are drawn to a circle from an external point, then the product of the lengths of the full secant segment and its external tangent segment is equal to the square of the length of the tangent segment. Students are then asked to find the missing segment lengths in given circles using these theorems.
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