Geometry: Intersecting Lines and Segment Measures

Objectives

• Students will investigate that if two chords of a circle intersect, the product of the segment lengths of one chord equals the product of the segment lengths of the other chord.
• Students will investigate that if two secant segments are drawn to a circle from an exterior point, then the product of the lengths of one secant segment and its external secant segment equals the product of the lengths of the other secant segment and its external secant segment.
• Students will investigate that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the tangent segment length equals the product of the lengths of the secant segment and its external secant segment.
• Students will investigate that if two segments from the same exterior point are tangent to a circle, then they are congruent.

Vocabulary

• chord
• secant
• tangent

About the Lesson

This lesson involves manipulating 2 intersecting lines that intersect with a circle at 1 or 2 points. As a result students will:

• Infer the relationship between the segment lengths of each chord.
• Observe the relationship between the products of the segment lengths of each chord.
• Observe lengths and infer relationships regarding the segment measures of a secant-secant intersection, a secant-tangent intersection, and a tangent-tangent intersection.