   Chapter 7.CT, Problem 9CT 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

Which of the following must be concurrent at an interior point of any triangle? angle bisectors perpendicular bisectors of sides altitudes medians

To determine

To find:

Which must be concurrent at an interior point of any triangle from the given options.

Explanation

To find which of the following must be concurrent at an interior point of any triangle.

Calculation:

Angle bisector:

The point of concurrency of the angle bisectors of a triangle is known as the incenter of a triangle. The incenter will always be located inside the triangle.

The point where the three internal angle bisectors of a triangle are concurrent is called the incentre of the triangle.

Perpendicular bisectors of sides:

The circumcenter is the point on concurrency of the perpendicular bisectors of the sides of a triangle. The point of concurrency is not necessarily inside the triangle. It may actually be in the triangle, on the triangle or outside of the triangle.

Altitudes:

The point of concurrency for the three altitudes for a given triangle is orthocenter.

The point of concurrency is not necessarily inside the triangle...

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