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Circular triangles with a mixture of convex and concave edges. In geometry, a circular triangle is a triangle with circular arc edges. Examples
A curvilinear triangle is a shape with three curved sides, for instance, a circular triangle with circular-arc sides. (This article is about straight-sided triangles in Euclidean geometry, except where otherwise noted.) Triangles are classified into different types based on their angles and the lengths of their sides.
Circular segment - the part of the sector that remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary. Scale of chords; Ptolemy's table of chords; Holditch's theorem, for a chord rotating in a convex closed curve; Circle graph; Exsecant and excosecant
In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter .
Euclid's definition of a circle is: ... About every triangle a unique circle, ... where r is the circle's radius, its length in taxicab geometry is 2r. Thus, a circle ...
In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are:
A Reuleaux triangle is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. [1] It is formed from the intersection of three circular disks , each having its center on the boundary of the other two.
In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] = or equivalently + + =, where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively).
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