# simelo-math

committed 15afd5b

[IMO] Adding .euk files et al. for IMO-2007-P2-P4, IMO-2011-P6, IMO-2012-P1

# IMO/2007/imo2k7p2.euk

`+`
`+A B C D parallelogram`
`+`
`+locus E(t = 0.1 to 0.9 step 20)`
`+  F = barycenter(C, t, D, 1 - t)`
`+  l = line(A, F)`
`+  G = intersection(l, line(B, C))`
`+  put center(circle(C, F, G))`
`+end`

# IMO/2007/imo2k7p4.euk

`+A B C triangle`
`+b = bisector(A, C, B)`
`+c = circle(A, B, C)`
`+K = midpoint(segment(B, C))`
`+L = midpoint(segment(A, C))`
`+O = center(c)`
`+P = intersection(b, line(K, O))`
`+Q = intersection(b, line(L, O))`
`+C R intersection(b, c)`
`+`
`+frame(-4, -4, 8, 6)`
`+`
`+draw(A, B, C)`
`+draw(segment(C, R))`
`+draw(segment(O, K))`
`+draw(segment(O, L))`
`+draw(segment(R, L))`
`+draw(segment(R, K))`
`+draw(c)`
`+draw(segment(O, Q))`
`+draw(segment(O, P))`
`+`
`+draw("\$A\$", A, -130:)`
`+draw("\$B\$", B, -50:)`
`+draw("\$C\$", C, 130:)`
`+draw("\$O\$", O, -50:)`
`+draw("\$P\$", P, 0.1, -160:)`
`+draw("\$Q\$", Q, 0.1, 50:)`
`+draw("\$R\$", R, -130:)`
`+draw("\$K\$", K, 50:)`
`+draw("\$L\$", L, 130:)`
`+`
`+mark(A, C, R)`
`+mark(R, C, B)`
`+`
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# IMO/2007/imo2k7p4.ps

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Add a comment to this file

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# IMO/2007/imo2k7p4_blog.euk

`+`
`+A B C triangle`
`+`
`+l = bisector(B, C, A)`
`+c = circle(A, B, C)`
`+C R intersection(l, c)`
`+P = intersection(l, perpendicular(segment(B, C), midpoint(segment(B, C)) ))`
`+Q = intersection(l, perpendicular(segment(A, C), midpoint(segment(A, C)) ))`
`+K = midpoint(segment(B, C))`
`+L = midpoint(segment(A, C))`
`+`
`+frame(-4, -4, 8, 6)`
`+`
`+draw(A, B, C)`
`+draw(l)`
`+draw(c)`
`+draw(segment(K, P), dashed)`
`+draw(segment(L, Q), dashed)`
`+draw(segment(K, R), dashed)`
`+draw(segment(L, R), dashed)`
`+`
`+draw("\$A\$", A, -130:)`
`+draw("\$B\$", B, -50:)`
`+draw("\$C\$", C, 130:)`
`+draw("\$P\$", P, 0.1, -160:)`
`+draw("\$Q\$", Q, 0.1, 50:)`
`+draw("\$R\$", R, -130:)`
`+draw("\$K\$", K, 50:)`
`+draw("\$L\$", L, 130:)`
`+`
`+color(gray)`
`+mark(A, C, R)`
`+mark(R, C, B)`
`+`
Add a comment to this file

# IMO/2007/imo2k7p4_blog.ps

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# IMO/2007/imo2k7p4_iso.euk

`+A B C isosceles`
`+b = bisector(A, C, B)`
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`+% Q = intersection(b, line(L, O))`
`+C R intersection(b, c)`
`+`
`+frame(-4, -4, 8, 6)`
`+`
`+draw(A, B, C)`
`+draw(b)`
`+draw(segment(O, K))`
`+draw(segment(O, L))`
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`+draw(segment(R, K))`
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`+% draw(segment(O, Q))`
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`+`
`+draw("\$A\$", A, -130:)`
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`+draw("\$O\$", O, -50:)`
`+% draw("\$P\$", P, 0.1, -160:)`
`+% draw("\$Q\$", Q, 0.1, 50:)`
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`+draw("\$L\$", L, 130:)`
`+`
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# IMO/2007/imo2k7p4_iso.png

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`+  { pop 1.e10 } 				% return 1.e10 as infinit`
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`+ { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall`
`+  [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto`
`+  i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25`
`+  mul j l + S rmoveto}F i L j L stroke }F}F}F}F `
`+  grestore `
`+  pop pop `
`+} def`
`+%`
`+%gsave abs CLW add /a ED a 0 dtransform round exch round exch`
`+%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25`
`+%% DG/SR modification begin - Dec. 12, 1997 - Patch 2`
`+%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a`
`+%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a`
`+%% DG/SR modification end`
`+%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict`
`+%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1`
`+%% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)`
`+%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }`
`+%% def`
`+%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore`
`+%pop pop } def`
`+%% DG/SR modification end`
`+%`
`+/BeginArrow { `
`+  ADict begin 			% hold it local, for end see EndArrow`
`+  /@mtrx CM def `
`+  gsave `
`+  2 copy T `
`+  2 index sub neg exch `
`+  3 index sub exch Atan `
`+  rotate newpath `
`+} def`
`+%`
`+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict`
`+%`
`+/Arrow { `
`+  CLW mul add dup `
`+  2 div /w ED `
`+  mul dup /h ED `
`+  mul /a ED `
`+  { 0 h T 1 -1 scale } if `
`+  w neg h moveto `
`+  0 0 L w h L w neg a neg rlineto `
`+  gsave fill grestore `
`+} def`
`+%`
`+/ArrowD { % the sides are drawn as curves (hv 20071211)`
`+  CLW mul add dup `
`+  2 div /w ED `
`+  mul dup /h ED `
`+  mul /Inset ED `
`+  { 0 h T 1 -1 scale } if % changes the direction`
`+% we use y=w/h^2 * x^2 as equation for the control points`
`+% for the coordinates the arrow is seen from top to bottom`
`+% the bottom (tip) is (0;0)`
`+  w neg h moveto % lower left of >`
`+  w 9 div 4 mul neg h 3 div 2 mul`
`+  w 9 div neg       h 3 div  `
`+  0 0 curveto    % tip of >`
`+  w 9 div        h 3 div  `
`+  w 9 div 4 mul  h 3 div 2 mul`
`+  w h curveto % upper left of >`
`+  w neg Inset neg rlineto % move to x=0 and inset`
`+  gsave fill grestore `
`+} def `
`+%`
`+/Tbar { `
`+  CLW mul add /z ED `
`+  z -2 div CLW 2 div moveto `
`+  z 0 rlineto stroke `
`+  0 CLW moveto `
`+} def`
`+%`
`+/Bracket { `
`+  CLW mul add dup CLW sub 2 div `
`+  /x ED mul CLW add /y ED /z CLW 2 div def `
`+  x neg y moveto `
`+  x neg CLW 2 div L x CLW 2 div L x y L stroke `
`+  0 CLW moveto `
`+} def`
`+%`
`+/RoundBracket { `
`+  CLW mul add dup 2 div `
`+  /x ED mul /y ED /mtrx CM def `
`+  0 CLW 2 div T x y mul 0 ne { x y scale } if `
`+  1 1 moveto `
`+  .85 .5 .35 0 0 0 curveto `
`+  -.35 0 -.85 .5 -1 1 curveto `
`+  mtrx setmatrix stroke 0 CLW moveto `
`+} def`
`+%`
`+/SD { 0 360 arc fill } def`
`+%`
`+/EndDot { % DS is the dot size `
`+  { /z DS def } { /z 0 def } ifelse `
`+  /b ED 0 z DS SD b { 0 z DS CLW sub SD } if `
`+  0 DS z add CLW 4 div sub moveto } def`
`+%`
`+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {`
`+  /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto`
`+  load } if ] cvx newpath 3 1 roll T exec } def`
`+%`
`+%/NArray { `
`+%   aload length 2 div dup dup cvi eq not { exch pop } if /n exch`
`+%   cvi def `
`+%} def`
`+%`
`+/NArray { % holds the coordinates and on top of stack the showpoints boolean`
`+  /showpoints ED `
`+  counttomark 2 div dup cvi /n ED `
`+  n eq not { exch pop } if`
`+  showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse `
`+} def`
`+%`
`+/Line { `
`+  NArray n 0 eq not `
`+    { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def `
`+      n { Lineto } repeat `
`+      CP 4 2 roll ArrowB L pop pop `
`+    } if `
`+} def`
`+%`
`+/Arcto { `
`+  /a [ 6 -2 roll ] cvx def `
`+  a r `
`+  /arcto load stopped { 5 } { 4 } ifelse { pop } repeat `
`+  a `
`+} def`
`+%`
`+/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq`
`+  and { pop pop /n n 1 sub def } if } def`
`+/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }`
`+  repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1`
`+  ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1`
`+  moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto`
`+  Lineto pop pop closepath } ifelse } def`
`+/Diamond { `
`+  /mtrx CM def `
`+  T rotate `
`+  /h ED `
`+  /w ED `
`+  dup 0 eq { pop } { CLW mul neg `
`+    /d ED `
`+    /a w h Atan def `
`+    /h d a sin Div h add def `
`+    /w d a cos Div w add def } ifelse `
`+  mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div `
`+  /ArrowA { moveto } def `
`+  /ArrowB { } def `
`+  false Line `
`+  closepath mtrx setmatrix } def`
`+% DG modification begin - Jan. 15, 1997`
`+%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {`
`+%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2`
`+%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0`
`+%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx`
`+%setmatrix } def`
`+%`
`+/Triangle { `
`+  /mtrx CM def `
`+  translate `
`+  rotate /h ED 2 div /w ED `
`+  dup CLW mul /d ED `
`+  /h h d w h Atan sin Div sub def `
`+  /w w d h w Atan 2 div dup cos exch sin Div mul sub def `
`+  mark `
`+  0 d w neg d 0 h w d 0 d `
`+  /ArrowA { moveto } def `
`+  /ArrowB { } def `
`+  false `
`+  Line `
`+  closepath `
`+  mtrx`
`+% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)`
`+% setmatrix } def`
`+  setmatrix pop `
`+} def`
`+% DG/SR modification end`
`+%`
`+/CCA { `
`+  /y ED /x ED `
`+  2 copy y sub /dy1 ED `
`+  x sub /dx1 ED `
`+  /l1 dx1 dy1 Pyth def `
`+} def`
`+%`
`+/CC { `
`+  /l0 l1 def `
`+  /x1 x dx sub def `
`+  /y1 y dy sub def `
`+  /dx0 dx1 def `
`+  /dy0 dy1 def `
`+  CCA `
`+  /dx dx0 l1 c exp mul dx1 l0 c exp mul add def `
`+  /dy dy0 l1 c exp mul dy1 l0 c exp mul add def `
`+  /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def `
`+  /x2 x l0 dx mul m mul sub def`
`+  /y2 y l0 dy mul m mul sub def `
`+  /dx l1 dx mul m mul neg def `
`+  /dy l1 dy mul m mul neg def `
`+} def`
`+%`
`+/IC { `
`+  /c c 1 add def `
`+  c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse `
`+  /a a 2 mul 3 div 45 cos b exp div def `
`+  CCA `
`+  /dx 0 def `
`+  /dy 0 def `
`+} def`
`+%`
`+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def`
`+/NC { CC x1 y1 x2 y2 x y curveto } def`
`+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def`
`+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def`
`+/NAC { x2 y2 x y curveto CC x1 y1 } def`
`+/EAC { x2 y2 x y ArrowB curveto pop pop } def`
`+%`
`+/OpenCurve { `
`+  NArray n 3 lt `
`+    { n { pop pop } repeat } `
`+    { BOC /n n 3 sub def n { NC } repeat EOC } ifelse `
`+} def`
`+%`
`+/AltCurve { `
`+  { false NArray n 2 mul 2 roll `
`+    [ n 2 mul 3 sub 1 roll ] aload`
`+    /Points ED `
`+    n 2 mul -2 roll } `
`+  { false NArray } ifelse `
`+  n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse `
`+} def`
`+%`
`+/ClosedCurve { `
`+  NArray n 3 lt `
`+    { n { pop pop } repeat } `
`+    { n 3 gt { CheckClosed } if `
`+      6 copy n 2 mul 6 add 6 roll `
`+      IC CC x y moveto n { NC } repeat `
`+      closepath pop pop `
`+    } ifelse `
`+} def`
`+%`
`+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def`
`+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def`
`+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def`
`+%`
`+/FontDot { `
`+  DS 2 mul dup `
`+  matrix scale matrix concatmatrix exch matrix`
`+  rotate matrix concatmatrix exch `
`+  findfont exch makefont setfont `
`+} def`
`+%`
`+/Rect { `
`+  x1 y1 y2 add 2 div moveto `
`+  x1 y2 lineto `
`+  x2 y2 lineto `
`+  x2 y1 lineto`
`+  x1 y1 lineto `
`+  closepath `
`+} def`
`+%`
`+/OvalFrame { `
`+  x1 x2 eq y1 y2 eq or `
`+    { pop pop x1 y1 moveto x2 y2 L } `
`+    { y1 y2 sub abs x1 x2 sub abs 2 copy gt `
`+      { exch pop } { pop } ifelse `
`+      2 div exch { dup 3 1 roll mul exch } if `
`+      2 copy lt { pop } { exch pop } ifelse`
`+      /b ED `
`+      x1 y1 y2 add 2 div moveto `
`+      x1 y2 x2 y2 b arcto `
`+      x2 y2 x2 y1 b arcto`
`+      x2 y1 x1 y1 b arcto `
`+      x1 y1 x1 y2 b arcto `
`+      16 { pop } repeat `
`+      closepath `
`+    } ifelse `
`+} def`
`+%`
`+/Frame { `
`+  CLW mul /a ED `
`+  3 -1 roll `
`+  2 copy gt { exch } if `
`+  a sub /y2 ED `
`+  a add /y1 ED `
`+  2 copy gt { exch } if `
`+  a sub /x2 ED `
`+  a add /x1 ED `
`+  1 index 0 eq { pop pop Rect } { OvalFrame } ifelse `
`+} def`
`+%`
`+/BezierNArray { `
`+  /f ED `
`+  counttomark 2 div dup cvi /n ED `
`+  n eq not { exch pop } if `
`+  n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat `
`+  f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse `
`+} def`
`+%`
`+/OpenBezier { `
`+  BezierNArray `
`+  n 1 eq `
`+    { pop pop } `
`+    { ArrowA n 4 sub 3 idiv `
`+      { 6 2 roll 4 2 roll curveto } repeat `
`+      6 2 roll 4 2 roll ArrowB curveto } ifelse `
`+} def`
`+%`
`+/ClosedBezier { `
`+  BezierNArray `
`+  n 1 eq `
`+    { pop pop } `
`+    { moveto n 1 sub 3 idiv `
`+      { 6 2 roll 4 2 roll curveto } repeat `
`+      closepath } ifelse `
`+} def`
`+%`
`+/BezierShowPoints { `
`+  gsave `
`+  Points aload length 2 div cvi /n ED `
`+  moveto `
`+  n 1 sub { lineto } repeat `
`+  CLW 2 div SLW [ 4 4 ] 0 setdash stroke `
`+  grestore `
`+} def`
`+%`
`+/Parab { `
`+  /y0 ED /x0 ED /y1 ED /x1 ED `
`+  /dx x0 x1 sub 3 div def `
`+  /dy y0 y1 sub 3 div def `
`+  x0 dx sub y0 dy add x1 y1 ArrowA`
`+  x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB `
`+  curveto `
`+  /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def `
`+} def`
`+%`
`+/Grid { `
`+  newpath `
`+  /a 4 string def `
`+  /b ED /c ED /n ED `
`+  cvi dup 1 lt { pop 1 } if `
`+  /s ED `
`+  s div dup 0 eq { pop 1 } if `
`+  /dy ED s div dup 0 eq { pop 1 } if`
`+  /dx ED dy div round dy mul `
`+  /y0 ED dx div round dx mul `
`+  /x0 ED dy div round cvi `
`+  /y2 ED dx div round cvi `
`+  /x2 ED dy div round cvi `
`+  /y1 ED dx div round cvi `
`+  /x1 ED `
`+  /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def `
`+  /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def `
`+  b 0 gt { `
`+    /z1 b 4 div CLW 2 div add def`
`+%    /Helvetica findfont b scalefont setfont `
`+    /b b .95 mul CLW 2 div add def } if `
`+  systemdict /setstrokeadjust known `
`+    { true setstrokeadjust /t { } def }`
`+    { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add`
`+       exch itransform } bind def } ifelse `
`+  gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse `
`+  /i x1 def `