The **Centroid (G) **of a triangle is the common intersection of the
three medians. A median of a triangle is the segment** **from a vertex
to the midpoint of the opposite side.

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**for the script.

The **Orthocenter (H) **of a triangle is the common intersection of
the three lines containing the altitudes. An altitude is a perpendicular
segment from a vertex to the line of the opposite side.

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for the script.

The **Circumcenter (C)** of a triangle is the point in the plane equidistant
from the three vertices of the triangle. C lies on the perpendicular bisector
of each side of the triangle.

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for the script.

The **Circumcircle **(the circumscribed circle) of a triangle has
the circumcenter (C) of the triangle as its center.

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The **Incenter (I) **of a triangle is the point on the interior of
the triangle that is equidistant from the three sides. I lies on the angle
bisector of each angle of the triangle.

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for the script.

The **Incircle **(the inscribed circle) of a triangle has the incenter
(I) of the triangle as its center.

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for the script.

The **Medial** triangle is constructed by connecting the three midpoints
of the sides. It is similar to the original triangle and one-fourth of its
area.

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for the script.

The **Orthic** triangle is constructed by connecting the feet of the
altitudes.

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for the script.

To construct a **Square**, given a side.

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for the script.

To construct the **Pedal Triangle.**

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for the script.