Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![### Geometry Practice Problems
#### In Exercises 7–10, find the value of x. (See Example 2.)
**Problem 7:**
- Diagram: A circle is intersected by a tangent and a secant line.
- The length of the secant segment outside the circle is labeled as 10 units.
- The length of the tangent segment is labeled as 6 units.
- The segment inside the circle is labeled as \( x \).
- The remaining segment of the secant line from the point where it enters the circle to the opposite point of tangency is labeled 8 units.
**Problem 8:**
- Diagram: A circle is intersected similarly by a tangent and a secant line.
- The length of the secant segment outside the circle is labeled as 5 units.
- The length of the tangent segment is labeled as 4 units.
- The segment inside the circle is labeled \( x \).
- The remaining segment of the secant line from the point where it enters to the opposite point of tangency is labeled 7 units.
For both diagrams, use the tangent-secant segment relationship to solve for \( x \).
The relationship states that for a circle, if a tangent segment from a point outside the circle and a secant segment from the same point outside the circle intersect, the length of the tangent segment squared is equal to the product of the lengths of the entire secant segment and its external part.
\[ \text{Tangent segment}^2 = \text{External part of secant} \times \text{Total secant segment} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42779bdc-66e8-47e8-8a59-0cd69b39b8c3%2Feec6de27-f249-4ac8-a6ed-1d2265007117%2Fyeww0gc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Practice Problems
#### In Exercises 7–10, find the value of x. (See Example 2.)
**Problem 7:**
- Diagram: A circle is intersected by a tangent and a secant line.
- The length of the secant segment outside the circle is labeled as 10 units.
- The length of the tangent segment is labeled as 6 units.
- The segment inside the circle is labeled as \( x \).
- The remaining segment of the secant line from the point where it enters the circle to the opposite point of tangency is labeled 8 units.
**Problem 8:**
- Diagram: A circle is intersected similarly by a tangent and a secant line.
- The length of the secant segment outside the circle is labeled as 5 units.
- The length of the tangent segment is labeled as 4 units.
- The segment inside the circle is labeled \( x \).
- The remaining segment of the secant line from the point where it enters to the opposite point of tangency is labeled 7 units.
For both diagrams, use the tangent-secant segment relationship to solve for \( x \).
The relationship states that for a circle, if a tangent segment from a point outside the circle and a secant segment from the same point outside the circle intersect, the length of the tangent segment squared is equal to the product of the lengths of the entire secant segment and its external part.
\[ \text{Tangent segment}^2 = \text{External part of secant} \times \text{Total secant segment} \]
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