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Medians' theorem

Relates the medians and the sides of an arbitrary triangle. Median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. ... more

Relation between the sides of an Equilateral triangle and its circumradius and inradius

An equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; ... more

Ceva's theorem (lines from vertices to the opposite sides of a triangle)

Ceva’s theorem is a theorem about triangles in Euclidean plane geometry. Given a triangle ABC, let the lines AO, BO and CO ... more

Area of a Reuleaux triangle

A Reuleaux triangle is a curve of constant width,( the separation of two parallel lines tangent to the curve is independent of their orientation), based ... more

Stewart's Theorem

Stewart’s theorem yields a relation between the length of the sides of the triangle and the length of a cevian of the triangle. A cevian is any line ... more

Relation between the inradius and exradii of an equilateral triangle

an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; ... more

Hyperbolic law of cosines - 1st law

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

Area of an arbitrary inscribed triangle

Related to the length of the sides of the triangle and the radius of the circumcircle of the triangle.

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Area of an arbitrary triangle related to the incircle radius

The area related to the semi perimeter of the triangle and the radius of the inscribed circle.

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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

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