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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

Morley's trisector theorem

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral ... more

Law of cosines

The law of cosines relates the cosine of an angle to the opposite side of an arbitrary triangle and the length of the triangle’s sides.
The law ... more

Area of an arbitrary triangle

The area of an arbitrary triangle can be calculated from the two sides of the triangle and the included angle.
... more

Law of tangents for the triangles

The law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.The law of ... more

Napoleon's theorem

In geometry, Napoleon’s theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, ... more

Area of a triangle (by the tangent of an acute or obtuse angle of the triangle)

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. The area ... more

Triangles' trigonometric condition (related to the tangents of the half-angles)

Three positive angles “A”, “B”, and “C”, each of them less than 180°, are the angles of a triangle if and only if ... more

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

Length of internal bisector of an angle in triangle in relation to the opposite segments

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. If the internal ... more

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