   Chapter 7.2, Problem 6E 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

Which lines or line segments or rays must be drawn or constructed in a triangle to locate itsa) incenter?b) circumcenter?

To determine

(a)

To find:

Which lines or line segments or rays must be drawn or constructed in a triangle to locate its incenter.

Explanation

Definition:

Angle bisector of a triangle:

The angle bisector of a triangle is a line segment that bisects one of the vertex angles of a triangle.

In general an angle bisector is equidistant from the sides of the angle when measured along a segment perpendicular to the sides of the angle.

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.

Given:

Which lines or line segments or rays must be drawn or constructed in a triangle to locate its incenter.

Calculation:

By the above definition,

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

For example:

To determine

(b)

To find:

Which lines or line segments or rays must be drawn or constructed in a triangle to locate its circumcenter.

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