   Chapter 7.2, Problem 33E 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

For what type of triangle will be the incenter and the circumcenter be the same.

To determine

To find:

For what type of triangle will be the incenter and the circumcenter be the same.

Explanation

Definition:

Equilateral triangle:

An equilateral triangle is a triangle in which all three sides are equal. An equilateral triangle is also equiangular that is all three internal angles are also congruent to each other and are each 60.

Incenter of the triangle:

The three angle bisectors of a triangle are concurrent and always meet in the triangle’s interior. The incenter is the center of the incircle. The incenter is the one point in the triangle whose distances to the sides are equal.

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

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