   Chapter 7.2, Problem 36E 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

Does a regular pentagon have (a) an incenter?.(b) a circumcenter?

To determine

(a)

To find:

Does a regular pentagon have an incenter.

Explanation

Definition:

Incenter of the triangle:

The three angle bisectors of a triangle are concurrent and always meet in the triangle 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.

Given:

Does a square have an incenter.

Clarification:

By the above definition,

The point of concurrence for the three angle bisectors of a triangle is known as incenter of the

triangle.

And also in regular pentagon, the angle bisectors are congruent. And regular pentagon is a regular polygon because they are both equilateral and equiangular. So the regular pentagon has an incenter...

To determine

(b)

To find:

Does a regular pentagon have a circumcenter.

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