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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

One of the legs of a right triangle related to the inradius and the other leg.

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more

Capstan equation ( belt friction equation)

The capstan equation or belt friction equation, also known as Eytelwein’s formula, relates the hold-force to the load-force if a flexible line is ... more

1st medians' theorem - Apollonius' theorem

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

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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

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

Inradius of arbitrary triangle

The radius of the inscribed circle of an arbitrary triangle is related to the altitudes of the triangle

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Pythagorean theorem (arbitrary triangle - acute angle)

Generalization of the Pythagorean theorem for the side opposite of the acute angle of an arbitrary triangle

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Pythagorean theorem (arbitrary triangle - obtuse angle)

Generalization of the Pythagorean theorem for the side opposite of the obtuse angle of an arbitrary triangle

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Product of the inradius and circumradius of a triangle

A 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 called ... more

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