Triangle+Centers

toc =Orthocenter=

The orthocenter is the point of concurrency of the three altitudes.

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=Circumcenter=

The circumcenter is the point of concurrency of the three perpendicular bisectors.

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How To Make The Circumscribed Circle, or A Circle Through Three Points
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How To Make The Triangle When Given The Circumcircle
Just draw a circle, then make a triangle. This is EASY!

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=Incenter=

The incenter is the point of concurrency of the three angle bisectors.

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How To Make The Inscribed Circle
There is just one circle I can construct that is tangent to the three sides of the triangle.

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How To Make The Triangle When Given The Incenter
This is one of the challenging "backwards" construction. Start by making a circle, then drawing in three radii, then constructing three perpendiculars, then using the intersection point tool to make the vertices.

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=Centroid=

The centroid is the point of concurrency of the three medians.

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How to Construct The Triangle Around the Median
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How To Construct the Triangle Around the Centroid
To do this, you must use the SYMMETRY TOOL three times. When you make your triangle, make sure the Centroid is closer to the side than the vertex.

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