Bsrgvty

documentclass[border=10pt]standalone
usepackagepst-eucl,pst-text,pstricks-add,pst-grad
usepackagemathptmx
begindocument
beginpspicture[showgrid](-5,-5)(10,5)
psframe*[fillstyle=solid,opacity=.5](-5,-5)(10,5)
pssetPointName=none,PointSymbol=none,linewidth=4.5pt,linejoin=2
pnodes(5;100)A(5;160)B(5;-55)C(0,0)O
pstCGravABCABCG
pstTriangleIC[linestyle=none]ABC
pstBissectBAC[linestyle=none]BACA'
pstBissectBAC[linestyle=none]ACBC'
pstInterLL[PointSymbol=square]AA'CC'I
pstMiddleABBCM
pstInterLLAIMOE
psline[linecolor=red!50](O)(E)(A)(M)
cnodeput[linestyle=none,fillstyle=solid,fillcolor=red!50](IC_O)I'textbfI
cnodeput[linestyle=none,fillstyle=solid,fillcolor=red!50](G)G'textbfG
cnodeput[linestyle=none,fillstyle=solid,fillcolor=red!50](O)O'textbfO
%%%
definecolorColorMhsb0.99999, 1, 1
definecolorColorNhsb0, 0, 1
pspolygon[linewidth=7pt,gradbegin=ColorM,gradend=ColorN](A)(B)(C) %% !?
pscircle(0,0)5
%%%%
pssetfillstyle=gradient,gradbegin=red!50!orange,gradend=yellow!70,gradangle=50
DeclareFixedFontRMT1ptmbn1.7cm
beginpscharclip[linewidth=0.1pt]%
 rput(3.25,2.75)RM Iranian% (3.25,2.75)!?
endpscharclip
beginpscharclip[linewidth=0.1pt]%
 rput(4.5,1.2)RM Geometry% (4.5,1.2)!?
endpscharclip
beginpscharclip[linewidth=0.1pt]%
 rput(5,-.25)RM Olympiad% (5,-.25)!?
endpscharclip
endpspicture
enddocument

The official image:

https://igo-official.ir/static/intro/images/logo.png

Question:

1. The gradient can be used for line ?


2. As the image ouput, I see the circle of I is smaller than G and O? How to fix?


3. See !? in the image output, how to delete the extra white space?


4. How to clip the part of content inside circle (I tried but it is failed.) and arrange it evenly?(See the official image)


5. I don't have the knowledge about font, so can anyone tell me know?

(Yes, not drawing exactly, only need approximately)

documentclassstandalone
usepackagepst-eucl,pst-text,pstricks-add,pst-grad
usepackagemathptmx
DeclareFixedFontRMT1ptmbn1.7cm%
begindocument
beginpspicture[showgrid=false](-5.2,-5.2)(10,5.2)
psframe*[fillstyle=solid,linecolor=black!40,opacity=.9](-5.2,-5.2)(10,5.2)
pscircle*[dimen=inner](0,0)5
%
 pssetfillstyle=solid,fillcolor=black!15,linecolor=black!15%
 rput[lb](0.5,-1)beginpscharclip[linewidth=0.1pt]%
 RMtabular[t]lIranian\~Geometry\~~Olympiadendtabular
 endpscharclip%

 pssetPointName=none,PointSymbol=none,linewidth=4.5pt,linejoin=2%
 pnodes(5;100)A(5;160)B(5;-55)C(0,0)O
 pstCGravABCABCG%
 pstTriangleIC[linestyle=none]ABC
 pstBissectBAC[linestyle=none]BACA'
 pstBissectBAC[linestyle=none]ACBC'
 pstInterLL[PointSymbol=square]AA'CC'I
 pstMiddleABBCM
 pstInterLLAIMOE
 psline[linecolor=red!50](O)(E)(A)(M)
 cnodeput[linestyle=none,fillstyle=solid,fillcolor=red!50](IC_O)I'textbfI
 cnodeput[linestyle=none,fillstyle=solid,fillcolor=red!50](G)G'textbfG
 cnodeput[linestyle=none,fillstyle=solid,fillcolor=red!50](O)O'textbfO
 %%%
 definecolorColorMhsb0.99999, 1, 1%
 definecolorColorNhsb0, 0, 1%
 pspolygon[linewidth=7pt,gradbegin=ColorM,gradend=ColorN,linecolor=black!20](A)(B)(C)
 psclippscircle[dimen=inner,linestyle=none](0,0)5
 pssetfillstyle=gradient,gradbegin=red!50!orange,gradend=yellow!70,gradangle=50%
 rput[lb](0.5,-1)beginpscharclip[linewidth=0.1pt]%
 RMtabular[t]lIranian\~Geometry\~~Olympiadendtabular
 endpscharclip%
 pscircle[dimen=inner,linecolor=red!40,fillstyle=none](0,0)5
 endpsclip
endpspicture
enddocument

endpscharclip needs a % at the end.
For the circle use dimen=inner. You can Times or Helvetica as font. The rest can be done by yourself ...

Why is the radius of I smaller:

documentclassarticle
usepackagemathptmx
DeclareFixedFontRMT1ptmbn1.7cm%
newsaveboxCBox
begindocument
begin tabularllll
& width & height & depth \hline
I globalsboxCBoxRM I & thewdCBox & thehtCBox & thedpCBox\

G globalsboxCBoxRM G & thewdCBox & thehtCBox & thedpCBox\

O globalsboxCBoxRM O & thewdCBox & thehtCBox & thedpCBox\
endtabular
enddocument

For I we need at least a diameter of 33,33 pt, but for G and O we need at least a diameter of 37,63 pt ...

for identical circle radius:

documentclass[pstricks,border=12pt]standalone
usepackagepst-node
begindocument
beginpspicture[showgrid=false](5,2)
 Cnodeput[radius=5mm](1,1)Leftfoovphantomg% to get the same height
 Cnodeput[radius=5mm](4,1)Rightright
endpspicture
enddocument