Calculating Segment Lengths Outside a Circle

Miacademy & MiaPrep Learning Channel

This geometry video lesson explores the mathematical relationships between segments that intersect outside of a circle. Building upon previous knowledge of intersecting chords, the video introduces the specific formulas needed to calculate segment lengths for three distinct scenarios: two secants, a secant and a tangent, and two tangents. The narrator guides viewers through the logic of the "Outside • Whole = Outside • Whole" formula and demonstrates how it applies uniquely to each case. The content covers how to set up and solve algebraic equations derived from geometric diagrams. Viewers learn how to identify the "outside" and "whole" portions of secant segments and how to treat tangent segments where the outside and whole lengths are identical. The video provides step-by-step example problems for each scenario, encouraging active participation by asking viewers to pause and solve for unknown variables like 'x'. This resource is highly valuable for high school geometry classrooms as it connects geometric theorems with algebraic practice. It clarifies common points of confusion—such as correctly determining the length of a whole secant segment—and offers a clear visual derivation of the "Two Tangents" theorem. The lesson is structured with clear objectives, practice problems, and a summary, making it an excellent tool for direct instruction or flipped classroom models.