Circumcenter of Triangle

What is Circumcenter of Triangle in Geometry?

Circumcenter of a triangle is a point belonging to the triangle which is the center of the circumcircle of the triangle.

What is the Formula of Circumcenter?

The formula for the circumcenter of the triangle is,

P(x, y) = {(x₁ sin 2A + x₂ sin 2B + x₃ sin 2C)/(sin 2A + sin 2B + sin 2c), (x₁ sin 2A + x₂ sin 2B + x₃ sin 2C)/(sin 2A + sin 2B + sin 2c)}

How to Find the Circumcenter of Triangle?

Circumcenter of a triangle is find using the intersection of the perpendicular bisector of any two lines of the triangle.

What is Difference Between Circumcenter and Incenter of Triangle?

Circumcenter of a triangle is the center of the circumcircle of the triangle where as incenter is the center of the encircle of the triangle.

Are Circumcenter and Centroid of Triangle the Same?

No, the circumcenter and centroid of a triangle are not the same. The circumcenter is the point where the perpendicular bisectors of the triangle’s sides intersect, while the centroid is the point where the triangle’s three medians intersect, typically located within the triangle.

The circumcenter of Triangle is a specific point where the perpendicular bisectors of the sides of the triangle intersect. This point is significant because it is equidistant from all three vertices of the triangle. It makes it the center of circle that can be circumscribed around the triangle which is known as circumcircle.

It is a point belonging to a triangle where the perpendicular bisector of the triangle meets. It is a point inside the triangle and is represented using P(x, y).

Let’s learn about the Circumcenter of triangle in detail, including its Definition, Properties and formula.