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Relation between the inradius and exradii of a right triangle

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

Length of internal bisector of an angle in triangle in relation to the opposite segments

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. If the internal ... more

Triangles' trigonometric condition (related to the tangents of the half-angles)

Three positive angles “A”, “B”, and “C”, each of them less than 180°, are the angles of a triangle if and only if ... more

Stewart's Theorem ( for triangle's bisectors)

Stewart’s theorem yields a relation between the length of the sides of the triangle and the length of a cevian of the triangle. A cevian is any line ... more

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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Relation between medians and circumradius for right triangle

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). Median of a triangle is a line ... more

Orthodiagonal quadrilateral (medians of the four triangles)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

Orthodiagonal quadrilateral (altitudes of the four triangles)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

Law of cotangents (in term of tangents)

In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. ... more

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