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Question: Writing text using textprint=true withe the draw command

Question:Writing text using textprint=true withe the draw command

das1404 135 Maple 7
geometry radical simplify simplification
March 30 2019
0

simplify_question.mws
Am trying to teach myself about lines and circles and inversion.  In the code below I'd like to put textt on the circles eg c1 to identify circle c1 etc.I'm more familiar with the textplot command & plottools, but want to use the draw command.  I've tried some options with the circle statement without success.
circle(c1,x^2+(y-2*R*cos(Pi/6))^2=R^2):  # 'ctext'=c1):

Is it possible to position text in a draw statement, similar to the textplot statement (that uses plot)?  

  I was amused by an idiosincracy of Maple 7.  The last line of my code uses the simplify command, yet I have had to resort to the simplification myself - (on the previous lines).   I was surprised and curious about this.  The Help section on simplify mentions several high power simplification procedures, yet fails to simplify a simple expression.  Any comments on this?

   I'm interested in learning more about circle inversion and wondered if anyone knew of some elementary books on this.  Geometry Inversion was never taught to me at school, nor university, despite it being a topic over 1000 years old.

   Thanks for your time.  Any comments, answers, gladly appreciated.      

  

> 

restart:
# # # # # # # # # # # # # # # # # # # # # # # # # # # #
# Test of geometry, radical axis.
# # # # # # # # # # # # # # # # # # # # # # # # # # # #
with(geometry):
with(plots):
_EnvHorizontalName := x: _EnvVerticalName := y:

R:=5:
circle(c1,x^2+(y-2*R*cos(Pi/6))^2=R^2):  # 'ctext'=c1):
circle(c2,(x-R)^2+y^2=R^2):
circle(c3,(x+R)^2+y^2=R^2):
RadicalAxis(ra12,c1,c2):
RadicalAxis(ra13,c1,c3):

printf("Colors:  c1=red c2=blue  c3=gold\n");
printf("       ra12=magenta    ra23=grey\n");
t1:=textplot([0, 1.8*R, `Circle c1`]):
draw([c1,c2, c3, ra12,ra13], axes=normal, color=[red, blue,gold, magenta,grey]);

#draw([c1,c2, c3, ra12,ra13,t1], axes=normal, color=[red, blue,gold, magenta,grey, black], printtext=true);
if AreTangent(c1,c2) then
   printf("Circles c1 and c2 are tangential, (as they all are!)\n");
end if:
testp:=Equation(ra12):
#print(whattype(testp));
printf("Equation of radical axis for c1 & c2 is %A or\n", testp);
simplify(Equation(ra12)/10);
simplify(Equation(ra12));

Warning, the name changecoords has been redefined

Colors:  c1=red c2=blue  c3=gold

       ra12=magenta    ra23=grey

Circles c1 and c2 are tangential, (as they all are!)

Equation of radical axis for c1 & c2 is 50+10*x-10*3^(1/2)*y = 0 or

5+x-sqrt(3)*y = 0

50+10*x-10*sqrt(3)*y = 0

  
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