   Chapter 7.2, Problem 9E 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, line segments, or rays are used to construct:a) The incircle of a triangle?b) The circumcircle of a triangle?

To determine

(a)

To find:

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

Explanation

Definition:

Incircle of a triangle:

The incircle of a triangle is the largest circle that fits in a triangle and its center is called the incenter of a triangle.

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 one point in the triangle whose distances to the sides are equal.

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.

Given:

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

Calculation:

By the above definition,

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

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