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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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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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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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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The Incircle (the inscribed circle) of a triangle has the incenter (I) of the triangle as its center.
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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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The Orthic triangle is constructed by connecting the feet of the altitudes.
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To construct a Square, given a side.
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To construct the Pedal Triangle.
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