Friday, 28 July 2017

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. 

Circumcentre of a Triangle

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. 

Circumcentre of a Triangle


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.' 


Circumcentre of a Triangle


Properties of Circumcentre of a Triangle

Property 1: Circumcentre of a triangle

The circumcenter is the centre of the circle which touches the three vertexes of the triangle. The circumcenter is said to circumscribe the triangle inside a circle. Circumscribing means that a circle passes through all the three vertices of a triangle. 

Circumcentre of a Triangle

Property 2: Circumcentre of a Triangle

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


Circumcentre of a Triangle

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. 

Circumcentre of a Triangle

Obtuse-angled Triangle:

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

Circumcentre of a 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

Circumcentre of a Triangle

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


Circumcentre of a Triangle

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.
Circumcentre of a Triangle
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