###### Asked in Geometry

Geometry

# When perpendicular bisectors of triangle share a common point of?

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## Related Questions

###### Asked in Math and Arithmetic, Geometry

### Is the three perpendicular bisector of a triangle intersect at a point in the exterior of the triangle true or false?

The three ANGLE bisectors of a triangle also bisect the sides,
and intersect at a point
INSIDE the triangle.
The angle bisectors are not necessarily perpendicular to
them.
The perpendicular bisectors of the sides can intersect in a
point either inside or outside
the triangle, depending on the shape of the triangle.

###### Asked in Algebra, Geometry

### 2 The intersection point of concurrency of the three perpendicular bisectors is called the?

Circumcenter.
The circumcenter of a triangle is the center of the circumcircle
of the triangle. It is the point, O, at which the perpendiculars
bisectors of the sides of a triangle are concurrent.
The circumcircle of a triangle is the circle that passes through
the three vertices. Its center is at the circumcenter.

###### Asked in Math and Arithmetic, Algebra, Geometry

### Name all types of triangles for which the point of concurrency is inside the triangle?

The answer depends on what point of concurrency you are
referring to. There are four segments you could be talking about in
triangles. They intersect in different places in different
triangles.
Medians--segments from a vertex to the midpoint of the opposite
side. In acute, right and obtuse triangles, the point of
concurrency of the medians (centroid) is inside the triangle.
Altitudes--perpendicular segments from a vertex to a line
containing the opposite side. In an acute triangle, the point of
concurrency of the altitudes (orthocenter) is inside the triangle,
in a right triangle it is on the triangle and in an obtuse triangle
it is outside the triangle.
Perpendicular bisectors of sides--segments perpendicular to each
side of the triangle that bisect each side. In an acute triangle,
the point of concurrency of the perpendicular bisectors
(circumcenter) is inside the triangle, in a right triangle it is on
the triangle and in an obtuse triangle it is outside the
triangle.
Angle bisectors--segments from a vertex to the opposite side
that bisect the angles at the vertices. In acute, right and obtuse
triangles, the point of concurrency of the angle bisectors
(incenter) is inside the triangle.

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