# Triangle V: How to solve questions asked on Circumcenter of a triangle?

In this post, we will discuss Circumcenter of a triangle that will help you solve geometric questions in SSC Exams.

Of the several centres of the triangle, the circumcenter of the triangle is the point where the perpendicular bisectors of a triangle intersect. The circumcenter is the point where the perpendicular bisectors of a triangle intersect. The circumcentre is also the centre of the triangle's circumcircle.

In this post, we will discuss in detail about all the properties of a circumcentre. But before moving on further have a quick review of Centroid and Orthocenter of a triangle which will help you save time in SSC Exams.

### What do you mean by Perpendicular Bisector?

A perpendicular bisector is a line that is perpendicular to the sides of a triangle and also bisects the sides into two equal halves.

Three perpendicular bisectors can be drawn in a triangle.

AD, BE and CF are the three perpendicular bisectors.

### What is a Circumcenter of a Triangle?

Circumcenter of a triangle is the point of intersection where all the perpendicular bisectors of a triangle intersect.

Circumcenter of a triangle is denoted by the letter 'S.'

### Property 2: Circumcentre of a Triangle

The angle made by the side BC with the circumcenter is 2 times the opposite angle.

### Property 3: Circumcentre of a Triangle

The position of the circumcentre of a triangle keeps on changing according to the type the triangle.

Acute angled Triangle:

In an Acute- angled triangle the circumcenter of a triangle lies inside the triangle.

Obtuse-angled Triangle:

In an Obtuse-angled triangle, the circumcenter of a triangle lies outside the triangle.

Right-angled Triangle:

In a Right-angled triangle, the circumcenter of a triangle lies on the hypotenuse of the triangle and it divides it into two equal halves.

r = AS or r = CS

In an equilateral triangle, the radius of a circle is,

Hope it's now easier for you to attempt questions that are based on the orthocentre of a triangle.

Do write in the comments section below on how this post has helped you understand the properties of Orthocentre of a triangle asked in mock tests for SSC CGL. Also, download free questionnaire for practice!

Stay tuned for our next blog.