Geometry 11.5 Solar Eclipses

11.5 Tangents and Secants Objectives Determine the relationship between a tangent line and a radius. Determine the relationship between congruent tangent segments. Prove the Tangent Segment Theorem. Prove the Secant Segment Theorem. Prove the Secant Tangent Theorem.

Problem 2: Tangent Segments Tangent Segment: A segment formed from an exterior point of the circle to the point of tangency. Together 1-3

Problem 2: Tangent Segments Tangent Segment Theorem: If two tangent segments are drawn from the same point on the exterior of a circle, then the tangent segments are congruent. Sketchpad Demo Tangent-Tangent Segments 𝑇𝑎𝑛 𝑆𝑒𝑔𝑚𝑒𝑛𝑡=𝑇𝑎𝑛 𝑆𝑒𝑔𝑚𝑒𝑛𝑡 Collaborate 5-6 (3 Minutes)

Problem 3: Secant Segments Secant Segment: Formed when two secants intersect in the exterior of a circle. Secant Segment: Begins at the point of intersection between two secants, continues into the circle, and ends at a point at which the secant intersects the circle. External Secant Segment: Part of the secant segment that lies outside the circle.

Problem 3: Secant Segments Together #1

Problem 3: Secant Segments Secant Segment Theorem: If two secants intersect in the exterior of a circle, then the product of the lengths of the secant segment and its external secant segment is equal to the product of the lengths of the second secant segment and its external secant segment. Sketchpad Demo Secant-Secant Segments 𝑆𝑒𝑐 1 ∙ 𝐸𝑥𝑡 1 = 𝑆𝑒𝑐 2 ∙ 𝐸𝑥𝑡 2

Problem 3: Secant Segments Together #3

Problem 3: Secant Segments Secant Tangent Theorem: If a tangent and a secant intersect in the exterior of a circle, then the product of the lengths of the secant segment and its external secant segment is equal to the square of the length of the tangent segment. Sketchpad Demo Secant-Tangent Segments 𝑆𝑒𝑐∙𝐸𝑥𝑡= 𝑇𝑎𝑛 2

Check for Understanding What kinds of lines do we have? 𝑆𝑒𝑐∙𝐸𝑥𝑡= 𝑇𝑎𝑛 2 8∙𝑑= 4 2 8𝑑=16 𝑑=2 𝑖𝑛𝑐ℎ𝑒𝑠

Formative Assessment Skills Practice 11.5 Vocabulary Pg. 817 (1-6) Pg. 818-828 (2-42) Even Due Today Tangent-Tangent Segments 𝑇𝑎𝑛 𝑆𝑒𝑔𝑚𝑒𝑛𝑡=𝑇𝑎𝑛 𝑆𝑒𝑔𝑚𝑒𝑛𝑡 Secant-Tangent Segments 𝑆𝑒𝑐∙𝐸𝑥𝑡= 𝑇𝑎𝑛 2 Secant-Secant Segments 𝑆𝑒𝑐 1 ∙ 𝐸𝑥𝑡 1 = 𝑆𝑒𝑐 2 ∙ 𝐸𝑥𝑡 2