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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 the circumcenter of the triangle, and its radius is called the circumradius .
Such a circle is said to circumscribe the points or a polygon formed from them; such a polygon is said to be inscribed in the circle. Circumcircle, the circumscribed circle of a triangle, which always exists for a given triangle. Cyclic polygon, a general polygon that can be circumscribed by a
The area of a regular heptagon inscribed in a circle of radius R is , while the area of the circle itself is ; thus the regular heptagon fills approximately 0.8710 of its circumscribed circle. Construction
English: Alternate method to determine the center of a circumscribed circle around a triangle: Choose a vertex angle, α; From the opposite side, draw a line that intersects at an angle of 90-α at one end; Draw another line that intersects at 90-α at the other end. The center of the circle is where the two added lines intersect.
The quadrature of the circle does not have a solid construction. A regular n-gon has a solid construction if and only if n=2 a 3 b m where a and b are some non-negative integers and m is a product of zero or more distinct Pierpont primes (primes of the form 2 r 3 s +1).
The nine-point circle is the circumscribed circle of the medial triangle, while the Spieker circle is the inscribed circle of the medial triangle. [2] With relation to their associated lines, the incenter for the Nagel line relates to the circumcenter for the Euler line. [ 1 ]
Bankoff circle – Circle formed from an arbelos, orthogonal to two of the semicircles of the arbelos and to a tangent circle within it; Brocard circle – Circle constructed from a triangle; Carlyle circle – Circle associated with a quadratic equation; Circumscribed circle (circumcircle) Midpoint-stretching polygon
The following is an animation from a neusis construction of a regular tridecagon with radius of circumcircle ¯ =, according to Andrew M. Gleason, [1] based on the angle trisection by means of the Tomahawk (light blue).