Properties of Circumcenter

While considering the triangle ABC with circumcenter O below, let’s discuss the various properties of circumcenter of a triangle.

• The circumcenter of a triangle is equidistant from all the vertices, i.e., OA = OB = OC.

• All the new triangles that are formed by joining the circumcenter of a triangle to its vertices are isosceles. ∆ AOB, ∆ BOC, and ∆ COA are isosceles triangles.

• In a triangle, if ∠A is acute or when O and A are on the same side of BC, then ∠BOC = 2 ∠A.

• In a triangle, if ∠A is obtuse or when O and A are on different sides of BC, then ∠BOC = 2(180° – ∠A).

• For an Acute-Angled Triangle, the circumcenter lies inside the triangle.

• In the case of an Obtuse-Angled Triangle, the circumcenter lies outside the triangle.

• For a Right-Angled Triangle, the circumcenter lies on the hypotenuse of the triangle.

The circumcenter of a Acute Angle Triangle, Right Angle Triangle, and Obtuse Angle Triangle can be understood with the help of diagram below:

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• Acute-Angled Triangle
• Obtuse-Angled Triangle
• Right-Angled 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.