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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Is it really necessary to construct all three bisectors of the angles of a triangle to locate its incenter?

To determine

To find:

To locate the incenter, is it necessary to construct all three bisectors of the angles.

Explanation

Definition:

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:

To locate the incenter, is it necessary to construct all three bisectors of the angles.

Calculation:

By the above definition,

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

The three bisectors of the angles all intersect at the same point so we only need two bisectors of the angles to locate it...

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