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Example 6: Is DC a tangent to OG? DG = 26 24 10

Example 6: Is DC a tangent to OG? DG = 26 24 10

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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**Notes 10.1 Circles and Tangent Lines** ### Example 6: **Is \( \overline{DC} \) a tangent to \( \odot G \)? \( DG = 26 \)** #### Diagram Explanation: - The diagram features a circle centered at point \( G \) with a radius of 10 units. - A point \( D \) exists outside the circle. - A line segment \( \overline{DC} \) extends from point \( D \), touching the circle at point \( C \). - The length \( \overline{DC} \) is labeled as 24 units. - The distance from \( D \) to \( G \) is given as 26 units. #### Conceptual Analysis: To determine if \( \overline{DC} \) is a tangent, verify if the Pythagorean Theorem holds: \[ DG^2 = DC^2 + GC^2 \] This holds true only if point \( C \) is the point of tangency, making \( \overline{DC} \) a tangent to the circle. ### Working with Tangents: Rule #3 [This would typically lead into a discussion of the specific rules or properties related to tangents in a subsequent section.]
Transcribed Image Text:**Notes 10.1 Circles and Tangent Lines** ### Example 6: **Is \( \overline{DC} \) a tangent to \( \odot G \)? \( DG = 26 \)** #### Diagram Explanation: - The diagram features a circle centered at point \( G \) with a radius of 10 units. - A point \( D \) exists outside the circle. - A line segment \( \overline{DC} \) extends from point \( D \), touching the circle at point \( C \). - The length \( \overline{DC} \) is labeled as 24 units. - The distance from \( D \) to \( G \) is given as 26 units. #### Conceptual Analysis: To determine if \( \overline{DC} \) is a tangent, verify if the Pythagorean Theorem holds: \[ DG^2 = DC^2 + GC^2 \] This holds true only if point \( C \) is the point of tangency, making \( \overline{DC} \) a tangent to the circle. ### Working with Tangents: Rule #3 [This would typically lead into a discussion of the specific rules or properties related to tangents in a subsequent section.]
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