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Euler's theorem (triangles)

The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is ... more

Length of the internal bisector of a triangle

An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half. The three angle bisectors intersect in a ... more

Relation between internal bisectors of angles A, B, and C of a triangle and its sides

An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant ... more

Theorem of internal triangle's bisector

The bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle

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Relation between the sides, the dinstances of the orthocenter from the vertices and the circumradius of a triangle

Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more

Area of a triangle (by the one side and the sines of the triangle's angles)

A triangle is a polygon with three edges and three vertices. In a scalene triangle, all sides are unequal and equivalently all angles are unequal. When the ... more

Euler line (its slope related to the slopes of the sides of a triangle)

In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more

Area of an arbitrary triangle (incircle and excircles)

The incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of ... more

Length of the medians of a triangle

Median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each ... more

2nd medians' theorem

Relates the projection of a median and the sides of an arbitrary triangle

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