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8. In the diagram below, circles A and B are tangent at point C and AB is drawn. Sketch all common tangent lines. Oo 9. Lines AE and BD are tangent to circles O and P at A, E, B, and D, as shown in the diagram below. If AC:CE-5:3, and BD-56, determine and state the length of CD.

8. In the diagram below, circles A and B are tangent at point C and AB is drawn. Sketch all common tangent lines. Oo 9. Lines AE and BD are tangent to circles O and P at A, E, B, and D, as shown in the diagram below. If AC:CE-5:3, and BD-56, determine and state the length of CD.

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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### Geometry Problems #### Problem 8: **Diagram Description:** The diagram shows two circles, labeled as \( A \) and \( B \), which are tangent to each other at point \( C \). A line segment \( \overline{AB} \) is drawn through point \( C \) and connects circle \( A \) to circle \( B \). **Task:** Sketch all common tangent lines for the given circles. #### Problem 9: **Diagram Description:** This diagram features two circles, labeled as \( O \) and \( P \), with the following lines and points: - \( AE \) and \( BD \) are straight lines. - \( AE \) is tangent to circle \( O \) at points \( A \) and \( E \). - \( BD \) is tangent to circle \( P \) at points \( B \) and \( D \). - The lines intersect at points \( A \), \( E \), \( B \), and \( D \). **Given:** - The ratio \( AC:CE \) is \( 5:3 \). - The length of \( BD \) is \( 56 \). **Task:** Determine and state the length of \( CD \). ### Explanation of Diagrams: **For Problem 8:** The diagram depicts two circles that touch each other at point \( C \). Since \( \overline{AB} \) is drawn through the point where they touch, the common tangents you need to sketch would be the tangents that can be drawn externally to both circles and the tangents that touch them internally at the point of tangency \( C \). **For Problem 9:** The second diagram involves two circles with tangents drawn from various points. The tangents \( AE \) and \( BD \) cross each other, and you are given a specific ratio for the segments of a line and a precise measurement for one of the segments, which you will use to find the length of \( CD \), using the properties and theorems related to circles and tangents. These activities require an understanding of the properties of tangent lines and circles, as well as the ability to apply ratios and algebra to solve for missing lengths.
Transcribed Image Text:### Geometry Problems #### Problem 8: **Diagram Description:** The diagram shows two circles, labeled as \( A \) and \( B \), which are tangent to each other at point \( C \). A line segment \( \overline{AB} \) is drawn through point \( C \) and connects circle \( A \) to circle \( B \). **Task:** Sketch all common tangent lines for the given circles. #### Problem 9: **Diagram Description:** This diagram features two circles, labeled as \( O \) and \( P \), with the following lines and points: - \( AE \) and \( BD \) are straight lines. - \( AE \) is tangent to circle \( O \) at points \( A \) and \( E \). - \( BD \) is tangent to circle \( P \) at points \( B \) and \( D \). - The lines intersect at points \( A \), \( E \), \( B \), and \( D \). **Given:** - The ratio \( AC:CE \) is \( 5:3 \). - The length of \( BD \) is \( 56 \). **Task:** Determine and state the length of \( CD \). ### Explanation of Diagrams: **For Problem 8:** The diagram depicts two circles that touch each other at point \( C \). Since \( \overline{AB} \) is drawn through the point where they touch, the common tangents you need to sketch would be the tangents that can be drawn externally to both circles and the tangents that touch them internally at the point of tangency \( C \). **For Problem 9:** The second diagram involves two circles with tangents drawn from various points. The tangents \( AE \) and \( BD \) cross each other, and you are given a specific ratio for the segments of a line and a precise measurement for one of the segments, which you will use to find the length of \( CD \), using the properties and theorems related to circles and tangents. These activities require an understanding of the properties of tangent lines and circles, as well as the ability to apply ratios and algebra to solve for missing lengths.
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