In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called...

right angle at the apex and the hypotenuse as the base; conversely, the circumcircle of any right triangle has the hypotenuse as its diameter. This is Thales'...

length of the sides equals the radius of the circumscribed circle or circumcircle, which equals 2 3 {\displaystyle {\tfrac {2}{\sqrt {3}}}} times the apothem...

cyclic polygon, and the circle is called its circumscribing circle or circumcircle. All concyclic points are equidistant from the center of the circle....

opposite angles (see figure 2), while R is the radius of the triangle's circumcircle. When the last part of the equation is not used, the law is sometimes...

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...

In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through...

points in the plane subdivides their convex hull into triangles whose circumcircles do not contain any of the points. This maximizes the size of the smallest...

perpendicular bisectors of its three sides, which is also the center of the circumcircle that passes through the three vertices). In an isosceles triangle with...

new points to form the decagon. Both in the construction with given circumcircle as well as with given side length is the golden ratio dividing a line...