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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

Area of a triangle (Heron's formula)

In geometry, Heron’s formula (sometimes called Hero’s formula), named after Hero of Alexandria, gives the area of a triangle by requiring no ... more

Regular Octagon Are ( 8 isosceles triangles)

Octagon is a polygon that has eight sides.
A regular octagon is a closed figure with sides of the same length and internal angles of the same size. ... 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 a triangle (Heron's formula) - alternative version

In geometry, Heron’s formula (sometimes called Hero’s formula), named after Hero of Alexandria, gives the area of a triangle by requiring no ... more

Pythagorean triangle ( hypotenuse)

A Pythagorean triangle is right angled and Heronian. Its three integer sides are known as a Pythagorean triple or Pythagorean triplet or Pythagorean triad. ... 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.

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1st medians' theorem - Apollonius' theorem

Relates the length of a median and the sides 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

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

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