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In Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any convex cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides. Its generalized version, Bretschneider's formula, can be used with non-cyclic quadrilateral.
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is ...
Cyclic quadrilateral. In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the ...
In elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle. It was introduced by Jakob Steiner in 1826. [1] Specifically, the power of a point with respect to a circle with center and radius is defined by. if is inside the circle, then .
The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle[2] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem, has a solution by an inductive method.