What are the coordinates of the incentre of a triangle?

Thread starter Garvit Goel
Start date May 13, 2011
Tags

Triangle

In summary, the incentre of a triangle is the point where all three angle bisectors intersect and is equidistant from all three sides of the triangle. It can be found by constructing the angle bisectors of the three angles of the triangle and is significant because it is the center of the triangle's incircle, which is the largest circle that can fit inside the triangle without crossing any of its sides. The inradius of a triangle is the distance from the incentre to any of the triangle's sides and is also the radius of the incircle. The incentre is used in various calculations in geometry and trigonometry, as well as in architecture and engineering for designing and constructing stable structures.

May 13, 2011

Garvit Goel

what are the coordinates of incentre of a triangle if the three vertices are (a1,b1),(a2,b2),(a3,b3)?

Mathematics news on Phys.org

May 13, 2011

micromass

Staff Emeritus

Science Advisor

Homework Helper

Insights Author

Wiki is your friend: http://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle

What is the definition of the incentre of a triangle?

The incentre of a triangle is the point where all three angle bisectors intersect. It is equidistant from all three sides of the triangle.

How is the incentre of a triangle found?

The incentre can be found by constructing the angle bisectors of the three angles of the triangle and finding their point of intersection.

What is the significance of the incentre of a triangle?

The incentre is significant because it is the center of the triangle's incircle, which is the largest circle that can fit inside the triangle without crossing any of its sides.

How is the incentre related to the inradius of a triangle?

The inradius of a triangle is the distance from the incentre to any of the triangle's sides. It is also the radius of the incircle.

What are some real-world applications of the incentre of a triangle?

The incentre is used in geometry and trigonometry for various calculations, such as finding the area of a triangle or determining the coordinates of its vertices. It is also used in architecture and engineering for designing and constructing stable structures.