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X is the center of one circle, Y is the center of the other. How do you know that triangle XYZ is equilateral?

X is the center of one circle, Y is the center of the other. How do you know that triangle XYZ is equilateral?

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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X is the center of one circle, Y is the center of the other. How do you know that triangle XYZ is equilateral?

This diagram shows two intersecting circles with labeled points X, Y, and Z. The circles intersect at points X and Y, which lie on the straight line segment XY. Point Z is positioned at the intersection of the two arcs above the line segment XY, forming a triangle XYZ. Each circle passes through point Z, with one circle centered on point X and the other on point Y, creating symmetry. **Explanation:** - **Points X and Y**: These are the points where the two circles intersect each other. - **Point Z**: This is the point where the arcs intersect above the line segment XY, forming the apex of triangle XYZ. - **Line Segment XY**: This is the base of triangle XYZ and is a straight line connecting points X and Y. - **Triangle XYZ**: Formed by connecting points X, Y, and Z. This diagram illustrates the geometric construction of a triangle using intersecting circles and their intersection points. This concept is commonly used in classical geometry and is known as the "triangular formation using intersecting circles."
Transcribed Image Text:This diagram shows two intersecting circles with labeled points X, Y, and Z. The circles intersect at points X and Y, which lie on the straight line segment XY. Point Z is positioned at the intersection of the two arcs above the line segment XY, forming a triangle XYZ. Each circle passes through point Z, with one circle centered on point X and the other on point Y, creating symmetry. **Explanation:** - **Points X and Y**: These are the points where the two circles intersect each other. - **Point Z**: This is the point where the arcs intersect above the line segment XY, forming the apex of triangle XYZ. - **Line Segment XY**: This is the base of triangle XYZ and is a straight line connecting points X and Y. - **Triangle XYZ**: Formed by connecting points X, Y, and Z. This diagram illustrates the geometric construction of a triangle using intersecting circles and their intersection points. This concept is commonly used in classical geometry and is known as the "triangular formation using intersecting circles."
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