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
Related questions
Question
![**Find the value of x in the following circles:**
### Diagrams:
1. **Diagram for Problem 4:**
- A right triangle is inscribed in a circle.
- The hypotenuse is labeled as 8 units.
- One leg is labeled as x and the other leg is labeled as 12 units.
2. **Diagram for Problem 5:**
- A right triangle is inscribed in a circle.
- The hypotenuse is labeled as 9 units.
- One leg is labeled as 4 units and the other leg is labeled as x units.
3. **Diagram for Problem 6:**
- A circle is divided by two perpendicular chords.
- One segment of a chord is labeled as 2, the adjacent segment is labeled as x, and the entire chord's segments are labeled as x + 1 and 6.
### Problems:
4) \( x = \) [Blank for the student to fill]
5) \( x = \) [Blank for the student to fill]
6) \( x = \) [Blank for the student to fill]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20047395-754f-4b4f-b55f-051358973abe%2Ffc5e5049-b2a2-4b15-a37a-be4965746215%2Fp515gte_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the value of x in the following circles:**
### Diagrams:
1. **Diagram for Problem 4:**
- A right triangle is inscribed in a circle.
- The hypotenuse is labeled as 8 units.
- One leg is labeled as x and the other leg is labeled as 12 units.
2. **Diagram for Problem 5:**
- A right triangle is inscribed in a circle.
- The hypotenuse is labeled as 9 units.
- One leg is labeled as 4 units and the other leg is labeled as x units.
3. **Diagram for Problem 6:**
- A circle is divided by two perpendicular chords.
- One segment of a chord is labeled as 2, the adjacent segment is labeled as x, and the entire chord's segments are labeled as x + 1 and 6.
### Problems:
4) \( x = \) [Blank for the student to fill]
5) \( x = \) [Blank for the student to fill]
6) \( x = \) [Blank for the student to fill]

Transcribed Image Text:**Find the value of x in the following circles:**
1. Circle with two intersecting chords:
- The first chord is split into segments measuring 6 and x.
- The second chord is split into segments measuring 12 and 8.
2. Circle with a tangent and a secant:
- The tangent segment measures 3.
- The secant is divided into two parts, with the external part measuring 5 and the internal segment labeled x.
3. Circle with two secants from a point outside the circle:
- One secant is divided into segments measuring 2 (external) and 4 (internal).
- The other secant's internal segment is labeled x.
**Solutions:**
1) \( x = \)
2) \( x = \)
3) \( x = \)
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