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2) 4x+2 4x 8

2) 4x+2 4x 8

Elementary Geometry For College Students, 7e
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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Find the Value of X

### Example Problem 2 In the diagram, a circle is divided by chords into several segments. Each chord is labeled with algebraic expressions or numeric values. - One chord is labeled \(4x + 2\). - Another segment adjacent to the first chord is labeled with the number \(9\). - Adjacent to the segment labeled \(9\) is another segment labeled \(8\). - A fourth segment, parallel to the first chord, is labeled \(4x\). The goal is to find the value of \(x\) that makes all the segments accurate representations within this circle. ### Explanatory Details: 1. **Understanding Chords**: - In a circle, a chord is a straight line connecting two points on the circumference of the circle. 2. **Properties to Use**: - In some problems involving chords, when two chords intersect each other, the products of the lengths of the segments of each chord are equal. This is the Power of a Point theorem. 3. **Calculating x**: - Apply the Power of a Point theorem or appropriate circle properties to find the value of \(x\). #### Approach: - For the given chords, assume they intersect at some point inside the circle. - Use the relationship: \((segment 1) \times (segment 2) = (segment 3) \times (segment 4)\). - Plug the given values and solve for \(x\). This diagram will help students understand how to solve for unknown variables within geometric figures by applying algebraic and geometric properties.
Transcribed Image Text:### Example Problem 2 In the diagram, a circle is divided by chords into several segments. Each chord is labeled with algebraic expressions or numeric values. - One chord is labeled \(4x + 2\). - Another segment adjacent to the first chord is labeled with the number \(9\). - Adjacent to the segment labeled \(9\) is another segment labeled \(8\). - A fourth segment, parallel to the first chord, is labeled \(4x\). The goal is to find the value of \(x\) that makes all the segments accurate representations within this circle. ### Explanatory Details: 1. **Understanding Chords**: - In a circle, a chord is a straight line connecting two points on the circumference of the circle. 2. **Properties to Use**: - In some problems involving chords, when two chords intersect each other, the products of the lengths of the segments of each chord are equal. This is the Power of a Point theorem. 3. **Calculating x**: - Apply the Power of a Point theorem or appropriate circle properties to find the value of \(x\). #### Approach: - For the given chords, assume they intersect at some point inside the circle. - Use the relationship: \((segment 1) \times (segment 2) = (segment 3) \times (segment 4)\). - Plug the given values and solve for \(x\). This diagram will help students understand how to solve for unknown variables within geometric figures by applying algebraic and geometric properties.
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