Question 1181244
<pre>
{{{drawing(400,400,-30,30,-30,30,

circle(0,0,40/sqrt(3)),line(0,40/sqrt(3),20,-20sqrt(3)+40/sqrt(3)),
circle(0,0,.3),

locate(18.3,20,8),
locate(13.3,12,12),  locate(5.5,16,20), locate(10,26,20),


line(20,-20sqrt(3)+40/sqrt(3),-6.180339887,-22.25166808),
locate(0,26,F), locate(20,26,E),locate(8,7,C),locate(21,-10,A),
locate(-7,-22.5,B),locate(17,17.4,D),




line(20,40/sqrt(3),0,40/sqrt(3)),line(-6.180339887,-22.25166808,20,40/sqrt(3))  )}}}


{{{FE^2}}}{{{""=""}}}{{{ED*EB}}}  tangent-secant theorem

{{{FE^2}}}{{{""=""}}}{{{ED*(ED+DB)}}}
{{{20^2}}}{{{""=""}}}{{{8*(8+DB)}}}
{{{400}}}{{{""=""}}}{{{8*(8+DB)}}}
{{{50}}}{{{""=""}}}{{{8+DB}}}
{{{42}}}{{{""=""}}}{{{DB}}}

{{{CB}}}{{{""=""}}}{{{DB-DC}}}
{{{CB}}}{{{""=""}}}{{{42-12}}}
{{{CB}}}{{{""=""}}}{{{30}}}

{{{DC*CB}}}{{{""=""}}}{{{FC*CA}}}  intersecting chords theorem
{{{12*30}}}{{{""=""}}}{{{20*CA}}}
{{{360}}}{{{""=""}}}{{{20*CA}}}
{{{18}}}{{{""=""}}}{{{CA}}}

Chord {{{FA}}}{{{""=""}}}{{{FC + CA}}}{{{""=""}}}{{{20+18}}}{{{""=""}}}{{{38}}}

Edwin</pre>