**Inscription of a circle into a four-cornered
**

Figure 1 shows part of a circle inscribed in a 4x4 square with the length *a*.
*V* and *W* are crossing-points of the mid-lines of the square with *
RS* and *ST *resp*.*. *b* is the distance from *V* to *Z* equal
*W* to *Z*.
Alpha corresponds to the angle in-between *WZ* and *YZ*.

Figure 2 shows the “perspective” view of a 8x8 square including center-lines (red) corresponding to inclinations of 30, 60 and 90 degree, and a frame-work of tangents (blue) suitable for the circle to be inscribed.

Figure 3 shows the grid with the circle inscribed.

Figure 4 and 5 present photographic equivalents

**Conclusions :**

The distance *b* - estimated as shown in the graph - is *b* = 1.008
*a*, thus *b* less than 1 % longer than *a*. The angle *
alpha* - estimated as shown the graph - is 29 degree and 45 “, thus less than
1 % different from 30 degree.

*V* and *W* are therefore suitable points of repair for drawing the
segment of a circle in such a square, *RS* and *SW* present
suitable tangents to this circle segment in *V* and *W, *and the angle
in-between* WZ YZ is *suitable to present an angle of 30 degree*, *he
concept thus suitable for situations requesting high
accuracy.