   Chapter 7.2, Problem 5E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

a) What is the general name of the point of concurrence for the three perpendicular bisectors of the sides of a triangle?b) What is the general name of the point of concurrence for the three medians of a triangle?

To determine

(a)

To find:

The general name of the point of concurrence for the three perpendicular bisectors of the sides of a triangle.

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:

The general name of the point of concurrence for the three perpendicular bisectors of the sides of a triangle.

Calculation:

By the above definition,

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

For example:

Let FS¯ and FR¯ name the perpendicular bisectors of sides BC¯ and AC¯, respectively. The point of concurrency F is equidistant from the endpoints of BC¯; thus, BF¯FC¯. In the same manner, AF¯FC¯

To determine

(b)

To find:

The general name of the point of concurrence for the three medians of a triangle.

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