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."

We will show how the triangle XYZ is an equilateral triangle as following

Answered: X is the center of one circle, Y is the…

Math

Geometry

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

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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Question

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."

Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.

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