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### Solve for \(x\) Below is a geometric diagram with a circle. There is a straight line cutting across the circle and an additional secant segment that extends outside the circle. Various lengths are labeled along the segments. #### Diagram Description: - Two secant segments intersect outside a circle. - The external segment length is labeled as `10`. - The respective internal segment length within the circle is labeled as `x`. - The other internal segment extending from the circle is labeled as `2`. - The internal segment in the circle, connected to the external segment `10`, is labeled as `98`. #### Explanation and Formula: When two secant segments intersect outside a circle, the following relationship holds: \( (External Segment + Internal Segment) \times External Segment = (Other External Segment + Internal Segment) \times Other External Segment \) In this case: \[ (x + 2) \times 2 = (10 + 98) \times 10 \] This equation can be solved to find the value of \( x \). #### Answer Box: \[ \text{Answer: } \] (Submit Answer button) Additional options are available for the submission, including an attempt limit of 2. --- By filling in the answer and submitting via the provided button, students can check their solution and validate their answer.

### Solve for \(x\) Below is a geometric diagram with a circle. There is a straight line cutting across the circle and an additional secant segment that extends outside the circle. Various lengths are labeled along the segments. #### Diagram Description: - Two secant segments intersect outside a circle. - The external segment length is labeled as `10`. - The respective internal segment length within the circle is labeled as `x`. - The other internal segment extending from the circle is labeled as `2`. - The internal segment in the circle, connected to the external segment `10`, is labeled as `98`. #### Explanation and Formula: When two secant segments intersect outside a circle, the following relationship holds: \( (External Segment + Internal Segment) \times External Segment = (Other External Segment + Internal Segment) \times Other External Segment \) In this case: \[ (x + 2) \times 2 = (10 + 98) \times 10 \] This equation can be solved to find the value of \( x \). #### Answer Box: \[ \text{Answer: } \] (Submit Answer button) Additional options are available for the submission, including an attempt limit of 2. --- By filling in the answer and submitting via the provided button, students can check their solution and validate their answer.

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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### Solve for \(x\) Below is a geometric diagram with a circle. There is a straight line cutting across the circle and an additional secant segment that extends outside the circle. Various lengths are labeled along the segments. #### Diagram Description: - Two secant segments intersect outside a circle. - The external segment length is labeled as `10`. - The respective internal segment length within the circle is labeled as `x`. - The other internal segment extending from the circle is labeled as `2`. - The internal segment in the circle, connected to the external segment `10`, is labeled as `98`. #### Explanation and Formula: When two secant segments intersect outside a circle, the following relationship holds: \( (External Segment + Internal Segment) \times External Segment = (Other External Segment + Internal Segment) \times Other External Segment \) In this case: \[ (x + 2) \times 2 = (10 + 98) \times 10 \] This equation can be solved to find the value of \( x \). #### Answer Box: \[ \text{Answer: } \] (Submit Answer button) Additional options are available for the submission, including an attempt limit of 2. --- By filling in the answer and submitting via the provided button, students can check their solution and validate their answer.
Transcribed Image Text:### Solve for \(x\) Below is a geometric diagram with a circle. There is a straight line cutting across the circle and an additional secant segment that extends outside the circle. Various lengths are labeled along the segments. #### Diagram Description: - Two secant segments intersect outside a circle. - The external segment length is labeled as `10`. - The respective internal segment length within the circle is labeled as `x`. - The other internal segment extending from the circle is labeled as `2`. - The internal segment in the circle, connected to the external segment `10`, is labeled as `98`. #### Explanation and Formula: When two secant segments intersect outside a circle, the following relationship holds: \( (External Segment + Internal Segment) \times External Segment = (Other External Segment + Internal Segment) \times Other External Segment \) In this case: \[ (x + 2) \times 2 = (10 + 98) \times 10 \] This equation can be solved to find the value of \( x \). #### Answer Box: \[ \text{Answer: } \] (Submit Answer button) Additional options are available for the submission, including an attempt limit of 2. --- By filling in the answer and submitting via the provided button, students can check their solution and validate their answer.
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