Solve for x.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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## Intersection of Chords

**Name:** Aracely Moreno  
**Topic:** Intersection of Chords  
**Date:** Jun 11, 9:23:18 AM

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### Solve for \( x \).

Below is a diagram of a circle with two intersecting chords. The lengths of the segments of the chords are labeled.

- One chord is divided into two segments of lengths 12 and \( x \).
- The other chord is divided into two segments of lengths 7 and 21. 

Diagram:

![Circle with intersecting chords labeled 12, x, 7, and 21](image_url)

### Solution

In a circle, when two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. This can be represented mathematically as:

\[ (12) \cdot (x) = (7) \cdot (21) \]

Simplifying the right-hand side:

\[ 12x = 147 \]

Solving for \( x \):

\[ x = \frac{147}{12} \]
\[ x = 12.25 \]

### Answer:

\[ x = 12.25 \]

### Submit your answer:

|  Answer:  | [_________] Submit Answer  |
|-----------|---------------------------|

---

**Note:** You have **1 attempt** out of 3 remaining.

---

*This instructional content is intended to help students understand how to solve problems involving the intersection of chords in a circle.*
Transcribed Image Text:## Intersection of Chords **Name:** Aracely Moreno **Topic:** Intersection of Chords **Date:** Jun 11, 9:23:18 AM --- ### Solve for \( x \). Below is a diagram of a circle with two intersecting chords. The lengths of the segments of the chords are labeled. - One chord is divided into two segments of lengths 12 and \( x \). - The other chord is divided into two segments of lengths 7 and 21. Diagram: ![Circle with intersecting chords labeled 12, x, 7, and 21](image_url) ### Solution In a circle, when two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. This can be represented mathematically as: \[ (12) \cdot (x) = (7) \cdot (21) \] Simplifying the right-hand side: \[ 12x = 147 \] Solving for \( x \): \[ x = \frac{147}{12} \] \[ x = 12.25 \] ### Answer: \[ x = 12.25 \] ### Submit your answer: | Answer: | [_________] Submit Answer | |-----------|---------------------------| --- **Note:** You have **1 attempt** out of 3 remaining. --- *This instructional content is intended to help students understand how to solve problems involving the intersection of chords in a circle.*
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