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Here is a diagram of a straightedge and compass construction. C is the center of one circle, and B is the center of the other. Explain why the length of segment BD is the same as the length of segment AB.

Here is a diagram of a straightedge and compass construction. C is the center of one circle, and B is the center of the other. Explain why the length of segment BD is the same as the length of segment AB.

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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Here is a diagram of a straightedge and compass construction. C is the center of one circle, and B is the center of the other. **Explanation:** This diagram shows two intersecting circles. The circle with center C is larger, and the circle with center B is smaller. The two circles intersect at points A and D. **Key Details:** - The point C is marked as the center of the larger circle. - The point B is the center of the smaller circle. - Segment BD lies along the line where the two circles intersect. - Segment AB is a straight line from point A (intersection) to point B (center of the smaller circle). **Task:** Explain why the length of segment BD is the same as the length of segment AB. **Additional Notes:** This construction uses principles of geometry to demonstrate properties of intersecting circles, specifically focusing on the congruency and symmetry resulting from the construction process.
Transcribed Image Text:Here is a diagram of a straightedge and compass construction. C is the center of one circle, and B is the center of the other. **Explanation:** This diagram shows two intersecting circles. The circle with center C is larger, and the circle with center B is smaller. The two circles intersect at points A and D. **Key Details:** - The point C is marked as the center of the larger circle. - The point B is the center of the smaller circle. - Segment BD lies along the line where the two circles intersect. - Segment AB is a straight line from point A (intersection) to point B (center of the smaller circle). **Task:** Explain why the length of segment BD is the same as the length of segment AB. **Additional Notes:** This construction uses principles of geometry to demonstrate properties of intersecting circles, specifically focusing on the congruency and symmetry resulting from the construction process.
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