No other point has this quality. Incenters, like centroids, are always inside their triangles. The above figure shows two triangles with their incenters and inscribed circles, or incircles circles drawn inside the triangles so the circles barely touch the sides of each triangle. The incenters are the centers of the incircles. The circumcenters are the centers of the circumcircles. You can see in the above figure that, unlike centroids and incenters, a circumcenter is sometimes outside the triangle.

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No other point has this quality. Incenters, like centroids, are always inside their triangles. The above figure shows two triangles with their incenters and inscribed circles, or incircles circles drawn inside the triangles so the circles barely touch the sides of each triangle. The incenters are the centers of the incircles. The circumcenters are the centers of the circumcircles.

You can see in the above figure that, unlike centroids and incenters, a circumcenter is sometimes outside the triangle. The circumcenter is Inside all acute triangles On all right triangles at the midpoint of the hypotenuse Finding the orthocenter Check out the following figure to see a couple of orthocenters. But get a load of this: Look again at the triangles in the figure.

Take the four labeled points of either triangle the three vertices plus the orthocenter. If you make a triangle out of any three of those four points, the fourth point is the orthocenter of that triangle. Pretty sweet, eh?

Orthocenters follow the same rule as circumcenters note that both orthocenters and circumcenters involve perpendicular lines — altitudes and perpendicular bisectors : The orthocenter is Inside all acute triangles.

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## Triangle Centers

The line segment created by connecting these points is called the median. You see the three medians as the dashed lines in the figure below. No matter what shape your triangle is, the centroid will always be inside the triangle. You can look at the above example of an acute triangle, or the below examples of an obtuse triangle and a right triangle to see that this is the case.

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## Difference Between Circumcenter, Incenter, Orthocenter and Centroid

Orthocenter The orthocenter is the point of intersection of the three heights of a triangle. A height is each of the perpendicular lines drawn from one vertex to the opposite side or its extension. Centroid The centroid is the point of intersection of the three medians. A median is each of the straight lines that joins the midpoint of a side with the opposite vertex The centroid divides each median into two segments, the segment joining the centroid to the vertex is twice the length of the length of the line segment joining the midpoint to the opposite side.

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## Orthocenter, Centroid, Circumcenter and Incenter of a Triangle

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## Incenter of a Triangle

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