The Circumcentre is the point of concurrency of the Perpendicular bisectors of the sides of a triangle. The circle passing through all the three vertices of the triangle with circumcentre (S) as centre is called circumcircle.

**Construction of the Circumcentre of a Triangle**

**Circumcentre**

The Circumcentre
is the point of concurrency of the Perpendicular bisectors of the sides of a triangle.

It is usually
denoted by *S*.

**Circumcircle**

The circle
passing through all the three vertices of the triangle with circumcentre (*S*)
as centre is called circumcircle.

**Circumradius**

The line
segment from any vertex of a triangle to the Circumcentre of a given triangle is
called circumradius of the circumcircle.

**Activity 11**

**Objective: **To construct a perpendicular bisector
of a line segment using paper folding.

**Procedure:** Make a line segment on a paper by folding
it and name it as *PQ*. Fold *PQ* in such a way that *P* falls on
*Q* and thereby creating a crease RS. This line *RS* is the perpendicular
bisector of *PQ*.

**Activity 12**

**Objective:** To locate the circumcentre of a triangle
using paper folding.

**Procedure:** Using Activity 12, find the perpendicular
bisectors for any two sides of the given triangle. The meeting point of these is
the circumcentre of the given triangle.

**Example 4.14**

Construct the circumcentre of the Δ*ABC *with* AB
*= 5 cm,* *∠*A *= 60º* *and ∠* B *= 80º. Also draw the circumcircle
and find the circumradius of the Δ*ABC.*

*Solution*

**Step 1 **

Draw the Δ*ABC *with the given measurements

**Step 2**

Construct
the perpendicular bisector of any two sides (*AC* and *BC*) and let them
meet at *S* which is the circumcentre.

**Step 3**

*S *as centre and* SA *=* SB *=*
SC *as radius, draw the Circumcircle to passes through *A*,*B* and
*C*.

Circumradius
= 3.9 cm.

**Note**

Where do the Circumcentre lie in the given triangles.

Tags : Example Solved Problems | Practical Geometry , 9th Maths : UNIT 4 : Geometry

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9th Maths : UNIT 4 : Geometry : Construction of the Circumcentre of a Triangle | Example Solved Problems | Practical Geometry

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