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The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters O_(AB), O_(BA), etc. of the six circumcircles of these smaller triangles ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

The pedal curve of a unit circle with parametric equation x = cost (1) y = sint (2) with pedal point (x,y) is x_p = cost-ycostsint+xsin^2t (3) y_p = ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

The Yff central circle, a term coined here for the first time, is the circumcircle of the Yff central triangle.

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

Determining the maximum number of pieces in which it is possible to divide a circle for a given number of cuts is called the circle cutting or pancake cutting problem. The ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

The Gershgorin circle theorem (where "Gershgorin" is sometimes also spelled "Gersgorin" or "Gerschgorin") identifies a region in the complex plane that contains all the ...