Chapter 7.2, Problem 5E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

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

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

To determine

(a)

**To find:**

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

Explanation

**Definition:**

Circumcenter:

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle. Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, the circumcenter is the point of concurrency of the three perpendicular bisectors of each side of the triangle.

**Given:**

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

**Calculation:**

By the above definition,

The point of concurrence for the three perpendicular bisectors of the sides of a triangle is known as circumcenter of the triangle.

For example:

Let

To determine

(b)

**To find:**

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

Sect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10E

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