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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

Bretschneider's formula - Area of a general quadrilateral

In geometry, Bretschneider’s formula is the shown expression for the area of a general quadrilateral.

A quadrilateral is a polygon with four ... more

Hyperbolic law of haversines

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more

Sum of the ratios on the three altitudes of the distance of the orthocenter from the base to the length of the altitude

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

Sine of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Cosine of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Tangent of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Law of sines (related to circumdiameter)

The law of sines, sine law, sine formula, or sine rule relates the sine of an angle to the opposite side of an arbitrary triangle and the diameter of the ... more

Semiperimeter of a triangle

The semi sum of the length of a triangle’s sides

... more

Volume of a pyramid (The base is a regular polygon)

A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid ... more

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