### Law of Sines

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. \[\frac{\overline{AB}}{\sin (C)}= \frac{\overline{BC}}{\sin (A)} =\frac{ \overline{CA}}{\sin (B)} = 2R\]