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| I did everything related to the [[ Mock AIME 3 Pre 2005]]
| | <asy> |
| all in one edit - each solution page, the answers, and the entire aime page.
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|
| | unitsize(.5cm); |
| | pair bar(pair a) { |
| | return (a.x,-a.y); |
| | }; |
| | pair A[] = { (6.5,0),(1.5,12) }; |
| | pair P[] = { A[0],A[1],-bar(A[1]),-bar(A[0]),(2A[0]-bar(A[0]))/3,(2A[0]+A[1])/3, |
| | (5A[0]-4bar(A[0]))/9,(5A[0]+4A[1])/9 |
| | }; |
| | pair D[] = { (2P[4]+P[5])/3,(P[4]+2P[5])/3 }; |
| | draw( D[0]--P[6] ,blue+1mm); |
| | draw( D[0]--P[4] ,blue+1mm); |
| | draw( P[6]--P[4], black+1mm); |
| | pair E[] = {(D[0]+P[6])/2,D[0] + P[6] - P[4]}; |
| | dot(E[0]);dot(E[1]); |
| | draw(P[6]--E[1],red+1mm); |
| | draw(P[4]--E[1],red+1mm); |
| | draw(P[4]--P[5]); |
| | draw( D[0] -- E[1]); |
| | draw(D[1]--P[7]); |
| | draw( P[3] -- P[0] -- P[1]) ; |
| | for(int i=0;i<10;++i) { |
| | if(i<4) { |
|
| |
|
| Hmmm... I think dollars signs convert automatically to math symbols
| | } else { |
| | | dot( (i<8) ? P[i] : D[i-8] ); |
| <pre> <math>ab</math> </pre>
| | } |
| <math>ab</math>
| | }; |
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| <asy>import graph;
| |
| import markers;
| |
| unitsize(3cm);
| |
| int n=18;
| |
| real a=360/n;
| |
| for (int i = -3; i < n-4; ++i)
| |
| {
| |
| draw(dir(i*a)--dir((i+1)*a),.5+black);
| |
| }
| |
| for (int i = -2; i < n-4; ++i)
| |
| {
| |
| draw(dir(i*a)--2*dir(i*a)-dir((i-1)*a),blue);
| |
| markangle(scale(.7)*"<math>\theta</math>",radius=15,2*dir(i*a)-dir((i-1)*a),dir(i*a),dir((i+1)*a),ArcArrow(1mm),.5+blue);
| |
| }
| |
| markangle(scale(.7)*"<math>\theta</math>",radius=15,2*dir(15*a)-dir(14*a),dir(15*a),dir(16*a),ArcArrow(1mm),.5+blue);
| |
| draw(dir(14*a)--6*dir(14*a)-5*dir(13*a));
| |
| label("<math>\ell</math>",(7*dir(14*a)-5*dir(13*a))/2,S);
| |
| label("<math>m</math>",(7*dir(15*a)-5*dir(14*a))/2,dir(3*a));
| |
| label(scale(.8)*"<math>180-\theta</math>",.95*dir(14*a),dir(5*a),red);
| |
| draw(dir(14*a)--6*dir(15*a)-5*dir(14*a));
| |
| markangle("<math>\theta</math>",radius=60,2*dir(14*a)-dir(13*a),dir(14*a),dir(15*a),ArcArrow(1mm),.5+red);
| |
| </asy> | | </asy> |
![[asy] unitsize(.5cm); pair bar(pair a) { return (a.x,-a.y); }; pair A[] = { (6.5,0),(1.5,12) }; pair P[] = { A[0],A[1],-bar(A[1]),-bar(A[0]),(2A[0]-bar(A[0]))/3,(2A[0]+A[1])/3, (5A[0]-4bar(A[0]))/9,(5A[0]+4A[1])/9 }; pair D[] = { (2P[4]+P[5])/3,(P[4]+2P[5])/3 }; draw( D[0]--P[6] ,blue+1mm); draw( D[0]--P[4] ,blue+1mm); draw( P[6]--P[4], black+1mm); pair E[] = {(D[0]+P[6])/2,D[0] + P[6] - P[4]}; dot(E[0]);dot(E[1]); draw(P[6]--E[1],red+1mm); draw(P[4]--E[1],red+1mm); draw(P[4]--P[5]); draw( D[0] -- E[1]); draw(D[1]--P[7]); draw( P[3] -- P[0] -- P[1]) ; for(int i=0;i<10;++i) { if(i<4) { } else { dot( (i<8) ? P[i] : D[i-8] ); } }; [/asy]](http://latex.artofproblemsolving.com/1/a/c/1acf167ef6b59f80eac30a664b77b608ac3cd9ea.png)
