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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

Tangential quadrilateral ( the sum of the opposite sides)

Product of the diagonals in a convex quadrilateral(Bretschneider's formula for diagonals)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. In any convex quadrilateral ABCD, the ... more

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.

... more

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

Cyclic quadrilateral (cosine of an angle)

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

Diameter of a triangle's circumscribed circle (related to the sides)

The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The circumcenter of a triangle ... more

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