Center Connected with Properties

The Centre of any shape is the primary part of that shape. In a simpler language, the centre is the middle part of any object. The Centre of any shape tells its point of symmetry. There are multiple types of centres, for this time the shape triangle has been taken to define the types of centres.

What is a centre?

According to the basic definition of the centre, there is a possibility that an object does not have a centre. The meaning of the centre can be different, in different shapes i.e., in a circle, the meaning of the centre is a single point that is equidistant from the edges of the circle whereas in a triangle there are multiple types of centres which are circumcentre, centroid, incentre, and orthocentre.

The centres in the shapes like squares, rhombus, rectangle, and parallelogram have their diagonals intersecting at a fixed point that is considered as their centre.

These centres are rotationally symmetrical. Similarly, also in shapes like ellipse and in hyperbola their axes intersect and the point where they intersect is referred to as their centre.

Properties of a triangle

A triangle has several unique properties and some of the basic properties of a triangle have been given below. 

• There are three sides in a triangle and there are three angles in the triangle
• The summation of the interior angles in the triangle is 180 degrees. 
• The summation of exterior angles of a triangle is 360 degrees.
• The summation of the two sides in the triangle is always greater than the side apart from the two.
• The difference between the sizes of any of the two sides in any triangle is less than the size of the side which is left.
• The opposite side of the largest angle in the triangle is always longest side the.
• Similarly, the opposite side to the largest interior angle Ina triangle is the longest side of a triangle.

Types of centres in a Triangle

The different types of centres present in a triangle are given below with the meaning of these centres.

Orthocentre of a Triangle

The orthocentre of a triangle is where the altitudes in the triangle intersect with each other; that point where the lines intersect is known as the orthocentre of that triangle. All these altitudes in the triangle begin from the corner (vertex) of the opposite of that particular triangle. Orthocentre is different for different types of a triangle that are Isosceles, scale, etc, 

Centroid in a Triangle

A centroid, in a triangle, can easily be defined as a point where there is an intersection of all medians from each side of that triangle. A median of a regular triangle can be referred to as a straight line that joins in the middle point of the other side of the vertex. It can also be referred to as the point of concurrency of medians in the triangle. The centroid in the triangle divides the triangle into two different segments. Due to the centroid, the triangle gets divided into the ratio of 2:1.

The circumcenter of a Triangle

The circumcenter of a triangle can be defined as the intersection point of the three perpendicular bisectors inside the triangle.

A perpendicular bisector is defined as a straight perpendicular line drawn from the middle point of the side in the triangle. The circumcenter of an acute angle triangle lies inside the circle whereas the circumcenter of the obtuse angle triangle lies outside the triangle. In a right-angled triangle, the circumcenter lies on the middle of the hypotenuse.

Incentre of a Triangle

The incenter of any triangle can be defined as the point where angle bisectors from the sides of the centroid meet (intersect). The angle bisector of any triangle divides that angle into two equal angles. The circle is inside a triangle, that is the incenter will always be equidistant from all three sides in the triangle.

Conclusion

As mentioned above, a centre is a very crucial part of any shape in geometry, it is used as a point of reference to define other properties of that shape. There is only one type of centre for a circle whereas in a triangle centre can be of different forms which all have been mentioned. There is also a FAQs section that provides additional information which will aid a better understanding of the topic.