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8) Kelly finds a problem in her Geometry homework with the given image and this information: BC = DE = 10, AF = 4z +1, and AG = 2z + 15. Which statements about chords could Kelly use to solve for x? Select all that apply. E D A If two chords intersect inside a circle, the sum of the lengths of the segments of one chord equals the sum of the lengths of the segments of the other chord. All chords have the same length as the diameter. A chord is a line that intersects a circle twice. Two chords are congruent if and only if they are equidistant from the center of the circle. If two chords intersect inside a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. A chord is a line segment with both endpoints on a circle.

8) Kelly finds a problem in her Geometry homework with the given image and this information: BC = DE = 10, AF = 4z +1, and AG = 2z + 15. Which statements about chords could Kelly use to solve for x? Select all that apply. E D A If two chords intersect inside a circle, the sum of the lengths of the segments of one chord equals the sum of the lengths of the segments of the other chord. All chords have the same length as the diameter. A chord is a line that intersects a circle twice. Two chords are congruent if and only if they are equidistant from the center of the circle. If two chords intersect inside a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. A chord is a line segment with both endpoints on a circle.

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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### Kelly's Geometry Problem on Chords **Problem Statement:** Kelly finds a problem in her Geometry homework with the given image and the following information: \( BC = DE = 10 \), \( AF = 4x + 1 \), and \( AG = 2x + 15 \). Which statements about chords could Kelly use to solve for \( x \)? Select all that apply. **Diagram Description:** The diagram depicts a circle with the points \( A \), \( B \), \( C \), \( D \), \( E \), \( F \), and \( G \) marked on it. The lines \( DE \) and \( BC \) are marked equal in length (both equal to 10). Line segments \( AF \) and \( AG \) are given by the expressions \( 4x + 1 \) and \( 2x + 15 \) respectively, indicating they are chords of the circle or segments intersecting inside the circle at point \( A \). **Statements to Consider:** 1. **Statement 1:** If two chords intersect inside a circle, the sum of the lengths of the segments of one chord equals the sum of the lengths of the segments of the other chord. 2. **Statement 2:** All chords have the same length as the diameter. 3. **Statement 3:** A chord is a line that intersects a circle twice. 4. **Statement 4:** Two chords are congruent if and only if they are equidistant from the center of the circle. 5. **Statement 5:** If two chords intersect inside a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. 6. **Statement 6:** A chord is a line segment with both endpoints on a circle. **Instructions:** Select all the statements that are applicable for Kelly to use to solve for \( x \).
Transcribed Image Text:### Kelly's Geometry Problem on Chords **Problem Statement:** Kelly finds a problem in her Geometry homework with the given image and the following information: \( BC = DE = 10 \), \( AF = 4x + 1 \), and \( AG = 2x + 15 \). Which statements about chords could Kelly use to solve for \( x \)? Select all that apply. **Diagram Description:** The diagram depicts a circle with the points \( A \), \( B \), \( C \), \( D \), \( E \), \( F \), and \( G \) marked on it. The lines \( DE \) and \( BC \) are marked equal in length (both equal to 10). Line segments \( AF \) and \( AG \) are given by the expressions \( 4x + 1 \) and \( 2x + 15 \) respectively, indicating they are chords of the circle or segments intersecting inside the circle at point \( A \). **Statements to Consider:** 1. **Statement 1:** If two chords intersect inside a circle, the sum of the lengths of the segments of one chord equals the sum of the lengths of the segments of the other chord. 2. **Statement 2:** All chords have the same length as the diameter. 3. **Statement 3:** A chord is a line that intersects a circle twice. 4. **Statement 4:** Two chords are congruent if and only if they are equidistant from the center of the circle. 5. **Statement 5:** If two chords intersect inside a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. 6. **Statement 6:** A chord is a line segment with both endpoints on a circle. **Instructions:** Select all the statements that are applicable for Kelly to use to solve for \( x \).
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