# Math's: Concurrent Lines: Concept, Angle Bisector of a Triangle and Perpendicular Bisector of the Sides of a Triangle

Get top class preparation for IMO-Level-2 right from your home: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 290K) ↧

## Concept of Concurrent Lines

**Three lines in a plane may:**

be parallel to each other, i.e., intersect in no point or

intersect each other in exactly one point or

intersect each other in two points or

intersect each other at the most in three points

Three or more lines in a plane which intersect each other in exactly one point, or which pass through the same point are called concurrent lines and the common point is called the point of concurrency.

## Angle Bisector of a Triangle

A line which divides an angle of a triangle into two equal parts is known as an angle bisector of the triangle. Since a triangle has three angles, we can draw three angle bisectors in it. are the three angle bisectors of given below.

All the three angle bisectors of a triangle pass through the same point, that is they are concurrent

The point of concurrency is called the ‘Incentre’ of the triangle.

Taking as the centre we can draw a circle touching all the three sides of the triangle called ‘Incircle’ of the triangle.

## Perpendicular Bisector of the Sides of a Triangle

A line which bisects a side of a triangle at right angle is called the perpendicular bisector of the side. Since a triangle has three sides, so we can draw three perpendicular bisectors in a triangle. are the three perpendicular bisectors of given below.

The three perpendicular bisectors of the sides of a triangle always pass through the same point, that is, they are concurrent.

The point of concurrency is called the ‘circumcenter’ of the triangle.

If we take O as the center and AO as the radius, we can draw a circle passing through the three vertices, A, B and C of the triangle, called ‘Circumcircle’ of the triangle.

It is to be noted here that the circumcenter will be

In the interior of the triangle for an acute triangle

On the hypotenuse for a right triangle and

In the exterior of the triangle for an obtuse triangle.