- 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 polygon,...
- cir****circle or cir****scribed circle, and the
vertices are said to be
concyclic. The
center of the
circle and its
radius are
called the cir****center and...
- that can be cir****scribed by a circle. The
vertices of this
polygon are
concyclic points. All
triangles are
cyclic polygons.
Cyclic quadrilateral, a special...
- the
other two. The
theorem is a
consequence of Ptolemy's
theorem for
concyclic quadrilaterals. Let a {\displaystyle a} be the side
length of the equilateral...
- In geometry, the ****anese
theorem states that the
centers of the
incircles of
certain triangles inside a
cyclic quadrilateral are
vertices of a rectangle...
- In geometry, the ****anese
theorem states that no
matter how one
triangulates a
cyclic polygon, the sum of
inradii of
triangles is constant.: p. 193 Conversely...
- In
Euclidean geometry, Ptolemy's
inequality relates the six
distances determined by four
points in the
plane or in a higher-dimensional space. It states...
-
Carnot (1753–1823). It is used in a
proof of the ****anese
theorem for
concyclic polygons.
Claudi Alsina,
Roger B. Nelsen: When Less is More: Visualizing...
- same
circle are
called concyclic, and a
polygon whose vertices are
concyclic is
called a
cyclic polygon.
Every triangle is
concyclic, but
polygons with more...
-
given triangle. It is so
named because it p****es
through nine
significant concyclic points defined from the triangle.
These nine
points are: The midpoint...
