   Chapter 7.2, Problem 9E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# Is it really necessary to construct all three perpendicular bisectors of the sides of a triangle to locate its circumcenter?

To determine

To find:

To locate the circumcenter, is it necessary to construct all three perpendicular bisectors of the sides.

Explanation

Definition:

Circumcenter:

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle. Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, the circumcenter is the point of concurrency of the three perpendicular bisectors of each side of the triangle

Given:

To locate the circumcenter, is it necessary to construct all three perpendicular bisectors of the sides.

Calculation:

By the above definition,

The point of concurrence for the three perpendicular bisectors of the sides is known as circumcenter of the triangle...

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