Assignment 4: Center Secrets of  Triangles

By Rebecca L. Adcock

Construct four centers of a triangle, the Centroid (G), the Orthocenter (H), the Circumcenter  (C) and the Incenter (I).


 The Centroid is the intersection of the three medians.

The dotted lines are the medians. A median is a line segment that connects the vertex with the midpoint of the opposite side.

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The Orthocenter is the point where the three altitudes of the triangle intersect.


The altitude is a perpendicular line segment from the vertex to the opposite side.

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The circumcenter is equidistant from all three vertices. It lies on the perpendicular bisectors of the three sides. Sometimes it lies outside the triangle. It is also the center of a circle (Circumcircle) that contains the vertices.


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The Incenter is equidistant from all three sides of the triangle. It lies on the angle bisectors. It is also the center of the inscribed circle (Incircle).


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Now let’s put all these centers into the same triangle and see how they relate to each other.

Here’s what I found:

This one is really great to play with.



We can construct triangles inside triangles. If we connect the midpoints of the sides of a triangle, the result is the medial triangle.



More discoveries:


Check it out for yourself.