Difference between Orthocenter and Circumcentre
The main difference is that orthocenter is the point where the three altitudes of a triangle intersect while circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.
Before we move to the differences, let’s understand what are Orthocenter and Circumcentre:
- Orthocenter: The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. An altitude is a line segment that passes through a vertex of the triangle and is perpendicular to the opposite side.
- Circumcentre: The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. A perpendicular bisector is a line segment that passes through the midpoint of a side of the triangle and is perpendicular to that side. The circumcenter is always located inside or on the triangle.
Now, let’s move to Orthocenter vs Circumcentre:
Major differences between Orthocenter and Circumcentre
|Orthocenter is the point where the three altitudes of a triangle intersect.||Circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.|
|Orthocenter may lie inside, outside, or on the triangle.||Circumcenter is always located inside or on the triangle.|
|Orthocenter is important for determining the height and steepness of a triangle.||Circumcenter is important for determining the symmetry and balance of a triangle.|
|Orthocenter can lie outside the triangle only for obtuse triangles.||Circumcenter always lies inside the triangle for all types of triangles.|
|The orthocenter is not necessarily equidistant from the vertices of the triangle.||The circumcenter is equidistant from the vertices of the triangle.|
Note that sometimes, the question might also be asked as “distinguish between Orthocenter and Circumcentre”.
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The orthocenter and circumcenter are two important points used in geometry to describe different properties of a triangle. These points have different characteristics and uses, such as determining the altitude or the center of the circle that circumscribes the triangle.
Understanding the differences between these two concepts can help us analyze and solve problems related to triangles in geometry.
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