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Q, R, and S are the centers of three circles. In this diagram, there are several equilateral triangles. How many?

Q, R, and S are the centers of three circles. In this diagram, there are several equilateral triangles. How many?

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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Q, R, and S are the centers of three circles. In this diagram, there are several equilateral triangles. How many?

The image is a geometric construction involving three overlapping circles. Here is a detailed description: 1. **Three Circles**: - The circles intersect each other and are of equal size. - The center of each circle is located at points W, V, and T. 2. **Triangle and Points**: - A triangle WVU is formed at the top of the construction, inscribed within the circle with center S. - Points Q, U, and R are collinear along a line segment QR that intersects the central area of the figure. - Q and R are highlighted in blue. 3. **Intersection Points**: - Point S is at the top center where two circles meet. - U is the central intersection point of all three line segments within the innermost section of the structure. - Lines connect W to V, V to T, and T to W, forming a larger triangle. In this construction, the interplay of triangles and circles highlights the symmetry and geometrical properties of intersecting circles and triangles. Each point and line segment plays a crucial role in maintaining the balance of the figure.
Transcribed Image Text:The image is a geometric construction involving three overlapping circles. Here is a detailed description: 1. **Three Circles**: - The circles intersect each other and are of equal size. - The center of each circle is located at points W, V, and T. 2. **Triangle and Points**: - A triangle WVU is formed at the top of the construction, inscribed within the circle with center S. - Points Q, U, and R are collinear along a line segment QR that intersects the central area of the figure. - Q and R are highlighted in blue. 3. **Intersection Points**: - Point S is at the top center where two circles meet. - U is the central intersection point of all three line segments within the innermost section of the structure. - Lines connect W to V, V to T, and T to W, forming a larger triangle. In this construction, the interplay of triangles and circles highlights the symmetry and geometrical properties of intersecting circles and triangles. Each point and line segment plays a crucial role in maintaining the balance of the figure.
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