Chapter 7.2, Problem 23E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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Is the circumcenter always located in the interior of the triangle?

To determine

**To find:**

Is the circumcenter always located in the interior of the 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:**

Is the circumcenter always located in the interior of the triangle.

**Clarification:**

The circumcircle of a triangle is the circle that passes through all vertices (corner point) of a triangle. That center is called the circumcenter, it can be fitted at inside or outside of the triangle.

The circumcenter is not always inside the triangle. In fact, it can be outside the triangle, as in the case of an obtuse triangle, or it can fall at the midpoint of the hypotenuse of a right triangle...

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