Geometry, Teacher\'s Edition

Segments of Chords, Secants, and Tangents

Chapter Study Sheet –This chapter contains many relationships for students to remember. It would be helpful
for them to summarize all of these relationships on a single sheet of paper to use when studying. Some instructors
allow students to use these sheets on the exam in order to encourage students to make the sheets. The value of a
study sheet is in its making. Students should know this and make them regardless of whether they can be used on
the exams. Sometimes if students know that they will be able to use the study sheet, they will not work to remember
all of the relationships, and their ability to learn the material is compromised. It is a hard issue to work around and
each instructor needs to deal with it as he or she feels best with their particular classes.

When to Add –When writing proportions involving secants, students will have a difficult time remembering to add
the two segments together to form the second factor. A careful study of the proof will help them remember this
detail. When they see secants, have them picture the similar triangles that could be drawn. Remind them, and give
them ample opportunity to practice.

Have Them Subtract –One way to give students more practice with the lengths of secants in circles is to give them
exercises where the entire length of the secant is given, and they have to setup an expression using subtraction to use
in the proportion.

Key Examples:

1. A secant and a tangent segment have a common exterior endpoint. The secant has a total length of 12 cm and the
   tangent has length 7 cm. What is the measure of the both segments of the secant?

Answer:

Let one segment of the secant bex, so the other can be represented by 20−x.

72 = ( 12 −x)∗ 12 The secant is composed of two segments

with approximate lengths of 4.1 cm and 7.9 cm

x≈ 7. 9

2. Two secant segments have a common endpoint outside of a circle. One has interior and exterior segments of
   lengths 10 ft and 12 ft respectively and the other has a total measure of 18 ft. What is the measure of the two
   segments composing the other secant?

Answer:

12 ( 10 + 12 ) = ( 18 −x)∗ 18 The secant is composed of two segments

with lengths 3

1

3

ft and 14

2

3

ft

x= 3

1

3

Chapter 2. Geometry TE - Common Errors