ATRACTOR

Given any triangle \([ABC]\), it is known that its perpendicular bisectors (lines whose points are equidistant from the ends of a side of the triangle) intersect at a point \(O\), called the circumcenter, which is equidistant from the vertices \(A\), \(B\) and \(C\), that is, such that \( \overline{OA} = \overline{OB} = \overline{OC}\). It is therefore possible to construct a circle with center at this point, passing through the three vertices of the triangle. The radius of this circle is called circumradius \((R)\).

The law of sines tells us that there is a proportionality between the length of each side of the triangle and the sine of the opposite angle, and the constant of proportionality is twice the circumradius. \[\frac{\overline{AB}}{\sin (C)}= \frac{\overline{BC}}{\sin (A)} =\frac{ \overline{CA}}{\sin (B)} = 2R\]