Chapter 7.2, Problem 7E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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

a) incenter?

b) Circumcenter?

c) orthocenter?

d) centroid?

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 triangleâ€™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.

To determine

(c)

**To find:**

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

To determine

(d)

**To find:**

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

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