Difference between Circumcentre and Incentre
In geometry, the terms “circumcenter” and “incenter” are used in relation to triangles. These terms describe different points associated with a triangle and have important properties that can be used to solve geometry problems.
The main difference is that the circumcenter is the center of the circle that circumscribes the triangle while the incenter is the center of the circle that inscribes the triangle.
Before we move to the differences, let’s understand what are Circumcentre and Incentre:
- Circumcentre: The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is the center of the circle that circumscribes the triangle, meaning that the circle passes through all three vertices of the triangle. The circumcenter is equidistant from the three vertices of the triangle.
- Incentre: The incentre is the point where the angle bisectors of the angles of a triangle intersect. It is the center of the circle that inscribes the triangle, meaning that the circle is tangent to all three sides of the triangle. The incenter is equidistant from the three sides of the triangle.
Now, let’s move to Circumcentre vs Incentre:
Major differences between Circumcentre and Incentre
| Circumcentre | Incentre |
|---|---|
| The circumcenter is equidistant from the three vertices of the triangle. | The incenter is equidistant from the three sides of the triangle. |
| The circumcenter lies outside the triangle. | The incenter lies inside the triangle. |
| The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle. | The incenter is the point of intersection of the angle bisectors of the angles of the triangle. |
| The circumcenter is equidistant from the vertices. | The incenter is equidistant from the sides of the triangle. |
| The circumcenter is the center of the circumcircle of the triangle. | The incenter is the center of the incircle of the triangle. |
That’s it.
Note that sometimes, the question might also be asked as “distinguish between Circumcentre and Incentre”.
Also see:
- Difference between Centre of Curvature and Radius of Curvature
- Difference between Orthocenter and Circumcentre
- Difference between Centre of Gravity and Centroid
Final words
Circumcenter and incenter are two important points associated with a triangle in geometry. These points have different characteristics and uses, such as determining the distance between the sides and vertices of a triangle or finding the radius of the inscribed and circumscribed circles of a triangle.
Knowing the differences between circumcenter and incenter can help us solve geometry problems more efficiently.
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