Chapter 7.2, Problem 23E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

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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