# What is the meaning of circumcenter of the triangle?

Table of Contents

## What is the meaning of circumcenter of the triangle?

Definition of circumcenter : the point at which the perpendicular bisectors of the sides of a triangle intersect and which is equidistant from the three vertices.

### What is special about circumcenter?

The circumcenter of a polygon is the center of the circle that contains all the vertices of the polygon, if such a circle exists. For a triangle, it always has a unique circumcenter and thus unique circumcircle.

#### What are the properties of the circumcenter of a triangle?

The circumcenter of triangle can be found out as the intersection of the perpendicular bisectors (i.e., the lines that are at right angles to the midpoint of each side) of all sides of the triangle. This means that the perpendicular bisectors of the triangle are concurrent (i.e. meeting at one point).

**Why is it called circumcenter?**

Circumcenter Theorem. All perpendicular bisectors of a triangle concur at one point called circumcenter as a center of its circumscribing circle.

**What is the definition of a circumcircle?**

Definition of circumcircle : a circle which passes through all the vertices of a polygon (such as a triangle)

## Is Circumcentre and centroid same?

The centroid divides each median into two segments, the segment joining the centroid to the vertex is twice the length of the length of the line segment joining the midpoint to the opposite side. The circumcenter is the point of intersection of the three perpendicular bisectors.

### What is a circumcenter created by?

perpendicular bisectors

When creating a circumcenter, we find the intersection of the perpendicular bisectors of each of the three sides of a triangle. This circumcenter is the center of the circle that circumscribes the shape.

#### What are the properties of the circumcenter of a triangle quizlet?

The circumcenter of a triangle is equidistant from all 3 vertices of a triangle. The incenter of a triangle is equidistant from all 3 sides of the triangle. The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side.

**What is the circumcenter and circumradius of a triangle?**

The hypotenuse of the triangle is the diameter of its circumcircle, and the circumcenter is its midpoint, so the circumradius is equal to half of the hypotenuse of the right triangle.

**What is circumcenter and centroid?**