# What is true about the circumcenter of a triangle?

## What is true about the circumcenter of a triangle?

The circumcenter is the centre of the circumcircle. All the vertices of a triangle are equidistant from the circumcenter. In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle.

What is the point of a circumcenter?

Circumcenter of triangle is the point where three perpendicular bisectors from the sides of a triangle intersect or meet. The circumcenter of a triangle is also known as the point of concurrency of a triangle.

### Why is it called circumcenter?

Any point equidistant from the end points of a segment lies on its perpendicular bisector. Since OA=OB=OC , point O is equidistant from A , B and C . This means that there is a circle having its center at the circumcenter and passing through all three vertices of the triangle. This circle is called the circumcircle .

What is always true about circumcenter?

For every acute triangle, the circumcenter is always inside the triangle. For every obtuse triangle, the circumcenter is always outside the triangle and always opposite the obtuse angle.

## Who was the circumcenter created by?

Sal Khan
Showing that the midpoint of the hypotenuse is the circumcenter. Created by Sal Khan.

Who discovered the circumcenter of a triangle?

It was not until the eighteenth century that mathematician Leonhard Euler (1707-1783) discovered a relationship between the three classical triangle centers. Euler discovered that in any triangle, the centroid, orthocenter and circumcenter are collinear (they lie on the same straight line).

### What 3 things make a circumcenter?

The Circumcenter of a triangle The point where the three perpendicular bisectors of a triangle meet. One of a triangle’s points of concurrency. One of several centers the triangle can have, the circumcenter is the point where the perpendicular bisectors of a triangle intersect.

Is circumcenter a centroid?

The centroid of a triangle is the point at which the three medians meet. The circumcenter is also the center of the circle passing through the three vertices, which circumscribes the triangle. This circle is sometimes called the circumcircle.

## Can the circumcenter be outside the triangle?

The circumcenter is not always inside the triangle. In fact, it can be outside the triangle, as in the case of an obtuse triangle, or it can fall at the midpoint of the hypotenuse of a right triangle.

Does every triangle have a circumcenter?

Theorem: All triangles are cyclic, i.e. every triangle has a circumscribed circle or circumcircle. (Recall that a perpendicular bisector is a line that forms a right angle with one of the triangle’s sides and intersects that side at its midpoint.) These bisectors will intersect at a point O.

### What is circumcenter and incenter?

circumcenter O, the point of which is equidistant from all the vertices of the triangle; incenter I, the point of which is equidistant from the sides of the triangle; orthocenter H, the point at which all the altitudes of the triangle intersect; centroid G, the point of intersection of the medians of the triangle.

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