geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle. A polygon whose vertices are concyclic is called a cyclic...

can be circumscribed by a circle. The vertices of this polygon are concyclic points. All triangles are cyclic polygons. Cyclic quadrilateral, a special...

because it passes through nine significant concyclic points defined from the triangle. These nine points are: The midpoint of each side of the triangle...

theorem No-three-in-line problem Incidence (geometry)#Collinearity Concyclic points Coplanarity The concept applies in any geometry Dembowski (1968, pg...

distances determined by four points in the plane or in a higher-dimensional space. It states that, for any four points A, B, C, and D, the following...

lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. Together with the...

applied to the segment AF, the points ARBF are concyclic (they lie on a circle). Similarly, the points AFCQ are concyclic. ∠ARB = 60°, so ∠AFB = 120°, using...

because it passes through nine significant concyclic points defined from the triangle. These nine points are: The midpoint of each side of the triangle...

midpoints of the sides and the feet of the four maltitudes are eight concyclic points; the eight point circle. The center of this circle is the centroid...

the circumcenter, the Lemoine point, and the first two Brocard points are concyclic—they all fall on the same circle, of which the segment connecting...