   Chapter 7.2, Problem 13E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

What point on a right triangle is the circumcenter of the right triangle?

To determine

To find:

What point on a right triangle is the circumcenter of the right 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:

What point on a right triangle is the circumcenter of the right triangle circumcircle of a triangle.

Calculation:

By the above definition,

The circumcenter is the center of circle which encloses a triangle and touches the three vertices of the triangle.

If it is a right triangle, the circumcenter has to be exactly half way along the hypotenuse.

Any right triangle will fit into a circle whose diameter is equal to the hypotenuse of the triangle, with all three vertices lying on the circle...

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