# Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams

### New York State Common Core Math Geometry, Module 5, Lesson 16

Worksheets for Geometry, Module 5, Lesson 16

Student Outcomes

• Students find “missing lengths” in circle-secant or circle-secant-tangent diagrams.

Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams

Classwork

Opening Exercise

Identify the type of angle and the angle/arc relationship, and then find the measure of 𝑥.

Exploratory Challenge 1

Measure the lengths of the chords in centimeters, and record them in the table.

Exploratory Challenge 2

Measure the lengths of the chords in centimeters, and record them in the table

Lesson Summary

THEOREMS:

• When secant lines intersect inside a circle, use 𝑎 ∙ 𝑏 = 𝑐 ∙ 𝑑.
• When secant lines intersect outside of a circle, use 𝑎(𝑎 + 𝑏) = 𝑐(𝑐 +𝑑).
• When a tangent line and a secant line intersect outside of a circle, use 𝑎2 = 𝑏(𝑏 + 𝑐)

Relevant Vocabulary

SECANT TO A CIRCLE: A secant line to a circle is a line that intersects a circle in exactly two point

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