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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

Radius of the circumcircle of a triangle

The radius of the circle on which lie a set of points is, by definition, the radius of the circumcircle of any triangle with vertices at any three of those ... more

2nd medians' theorem

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

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Sum of the ratios on the three altitudes of the distance of the orthocenter from the vertex 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

Equilateral triangle - semiperimeter

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also ... more

Hyperbolic law of cosines - 2nd 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

Cyclic quadrilateral (tangent of the acute angle between the diagonals)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... 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

Parallax

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or ... more

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