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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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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 a convex quadrilateral (in terms of sides and angle θ of the diagonals)

Quadrilateral is a polygon with four sides (or edges) and four vertices or corners. The area of a quadrilateral can be calculated by the sides and the ... more

Steadily rotating crank ( displacement of the end of the connecting rod )

A crank is an arm attached at right angles to a rotating shaft by which reciprocating motion is imparted to or received from the shaft. It is used to ... more

Length of an arc of a circle (central angle in radians)

Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex ... more

Ceva's theorem (lines from vertices to the opposite sides of a triangle)

Ceva’s theorem is a theorem about triangles in Euclidean plane geometry. Given a triangle ABC, let the lines AO, BO and CO ... more

Menelaus' theorem ( transversal line passes inside triangle )

Menelaus’ theorem, named for Menelaus of Alexandria, is a theorem about triangles in plane geometry. Given a triangle ABC, ... more

Length of the medians of a triangle

Median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each ... more

Regular Octagon Area ( related to the circumradius)

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

Perimeter of a Triangle

A perimeter is a path that surrounds a two-dimensional shape. The word comes from the Greek peri (around) and meter (measure). The term may be used either ... more

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