Derivation of Scott's Radius

How about;

R = (abc)/SQRT((a+b+c)(b+c-a)(c+a-b)(a+b-c))

Lindell equation and Zelenak equation are virtually the same. See pdf.

The original post;

https://surveyorconnect.com/threads/favorite-formulae.323093/

For the radius point coordinates from the original post;
Xrp=(ya²+xa²-yc²-xc²-(ya-yc)*(ya²+xa²-yb²-xb²)/(ya-yb))/2/(xa-xc-(ya-yc)*(xa-xb)/(ya-yb))
Yrp=(ya²+xa²-yb²-xb²-2*Xrp*(xa-xb))/(ya-yb)/2

and if your " ² " key is broken;
Xrp=((((yb-xa)/(xb-xa))*((yc-yb)/(xc-xb))*(ya-yc)+((yc-yb)/(xc-xb))*(xa+xb)-((yb-ya)/(xb-xa))*(xb+xc))*0.5/(((yc-yb)/(xc-xb))-((yb-ya)/(xb-xa))))
Yrp=(-1/((yb-ya)/(xb-xa))*(Xrp-((xa+xb)*0.5)))+((ya+yb)*0.5)

Reminds me of a song:

[MEDIA=youtube]_aVRWRQJZoE[/MEDIA]