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Describe the location of the point of concurrency of the perpendicular bisectors of a...

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busylizzy15 | (Level 2) Honors

Posted April 8, 2013 at 2:28 AM via web

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Describe the location of the point of concurrency of the perpendicular bisectors of a triangle.

l - on the longest side of the triangle.

2 - in the same place as the point of concurrency of the altitudes of the triangle.

3- always in the interior of the triangle

4 - in the exterior, on, or in the interior of the tirangle.

5 - none of the above

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 8, 2013 at 2:59 AM (Answer #1)

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The point of concurrency of the perpendicular bisectors of a triangle is known as the circumcenter. The circumcenter of any triangle is equidistant from the vertices of the triangle. This allows a circle to be drawn with the circumcenter as the center of the circle and the distance from any vertex to the circumcenter as the radius of the circle.

For acute triangles, which are triangles with all interior angles less than 90 degree, the circumcenter lies in the interior of the triangle. In a right triangle the circumcenter lies on the hypotenuse and in an obtuse triangle the circumcenter lies in the exterior of the triangle.

The correct option is 4.

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