Chapter 7.2, Problem 4E

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7th Edition

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ISBN: 9781337614085

Textbook Problem

a) What is the general name of the point of concurrence for the three angle bisectors of a triangle?

b) What is the general name of the point of concurrence for the three altitudes of a triangle?

To determine

(a)

**To find:**

The general name of the point of concurrence for the three angle bisectors of a triangle.

Explanation

**Definition:**

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:**

The general name of the point of concurrence for the three angle bisectors 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.

For example:

In above figure, the bisectors of

We know that

Similarly,

To determine

(b)

**To find:**

The general name of the point of concurrence for the three altitudes of a triangle.

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