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Area of a regular inscribed n-gon in a unit circle

The area of a regular n-gon with side s inscribed in a unit circle ( unit circle is a circle with radius of one). RESTRICTION: s<2

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Radius of an inscribed sphere in a circumscribed Regular Octahedron

An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at ... more

Relation between the inradius,exradii,circumradius and the distances of the orthocenter from the vertices 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

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

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

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

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

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

Cardioid ( X-coordinate)

A cardioid is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type ... more

Cardioid ( Y-coordinate)

A cardioid is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type ... more

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