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The "∅" symbol is always drawn as a slashed circle, whereas in most typefaces the letter "Ø" is a slashed ellipse. The diameter symbol ( ⌀ ) (Unicode character U+2300) is similar to the lowercase letter ø, and in some typefaces it even uses the same glyph , although in many others the glyphs are subtly distinguishable (normally, the ...
These circles can also be obtained by starting with a circle of radius R in the xy-plane, centered at (r,0,0) or (-r,0,0), and then rotating this circle about the x-axis by an angle of arcsin(r/R). A treatment along these lines can be found in Coxeter (1969). [1]
An oriented circle is an ordinary circle with an orientation represented by a binary value attached to it, which is either or . The only exception is a circle of radius zero, which has orientation equal to . A point is defined to be an oriented circle of radius zero.
The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference. Conversely, the perpendicular to a radius through the same endpoint is a tangent line. The resulting geometrical figure of circle and tangent line has a reflection symmetry about the axis of the radius.
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 circumradius respectively.
The word diagonal derives from the ancient Greek διαγώνιος diagonios, [1] "from corner to corner" (from διά- dia-, "through", "across" and γωνία gonia, "corner", related to gony "knee"); it was used by both Strabo [2] and Euclid [3] to refer to a line connecting two vertices of a rhombus or cuboid, [4] and later adopted into ...
One diagonal crosses the midpoint of the other diagonal at a right angle, forming its perpendicular bisector. [9] (In the concave case, the line through one of the diagonals bisects the other.) One diagonal is a line of symmetry. It divides the quadrilateral into two congruent triangles that are mirror images of each other. [7]
The radius of a triangle's circumcircle is twice the radius of that triangle's nine-point circle. [6]: p.153 Figure 3. A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle. Figure 4